# 壓縮映射定理基礎 · 脈衝 R01

本批已通過 Schema、去重、來源快照與獨立答案重算；仍未標記為人工審定。

本題庫已有對應的中英逐步詳解。原題的 candidate 與英文 ai_candidate 狀態保留；AI 覆核、有限計算與 Lean 形式證明分開標示。

batch-20261015-advance-20261116-r01-contraction-mapping-theorem-foundations · 2026-10-15 · 100 題

欄序為來源綁定的呈現補充；原始 JSONL 與數學答案不變。

[欄序與來源綁定資料](https://ocme.evemisslab.com/data/i18n/question-output-protocols.json)



## 1. 壓縮映射定理

完整metric、total self-map與forall-pairs q<1 contraction責任。操作=contract-metric-qualification；資料={"metric":[[0,1,3],[1,0,2],[3,2,0]],"mapping":[0,0,1],"q":[1,2]}。請依 [point_count, self_map, q, q_in_range, pair_inequality_rows, global_contraction, certificate] 欄序回答。

查看答案與解釋(3, 是, 1/2, 是, [[0, 0, 0, 0, 是], [0, 1, 0, 1/2, 是], [0, 2, 1, 3/2, 是], [1, 0, 0, 1/2, 是], [1, 1, 0, 0, 是], [1, 2, 1, 1, 是], [2, 0, 1, 3/2, 是], [2, 1, 1, 1, 是], [2, 2, 0, 0, 是]], 是, finite_metric_is_complete_but_full_pair_audit_is_still_required)

Wave6第十層核對=(3, 是, 1/2, 是, [[0, 0, 0, 0, 是], [0, 1, 0, 1/2, 是], [0, 2, 1, 3/2, 是], [1, 0, 0, 1/2, 是], [1, 1, 0, 0, 是], [1, 2, 1, 1, 是], [2, 0, 1, 3/2, 是], [2, 1, 1, 1, 是], [2, 2, 0, 0, 是]], 是, finite_metric_is_complete_but_full_pair_audit_is_still_required)；依完整明示資料獨立重算；Picard orbit、unique fixed point與geometric tail bound使用exact arithmetic；q=1、非self-map、noncomplete或sampled-pairs不足；finite model不取代一般定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r01-contraction-mapping-theorem-0001/)

壓縮映射定理 · qf-mod47-contract-metric-qualification · candidate





## 2. 壓縮映射定理

完整metric、total self-map與forall-pairs q<1 contraction責任。操作=contract-metric-qualification；資料={"metric":[[0,2,6],[2,0,4],[6,4,0]],"mapping":[0,0,1],"q":[1,2]}。請依 [point_count, self_map, q, q_in_range, pair_inequality_rows, global_contraction, certificate] 欄序回答。

查看答案與解釋(3, 是, 1/2, 是, [[0, 0, 0, 0, 是], [0, 1, 0, 1, 是], [0, 2, 2, 3, 是], [1, 0, 0, 1, 是], [1, 1, 0, 0, 是], [1, 2, 2, 2, 是], [2, 0, 2, 3, 是], [2, 1, 2, 2, 是], [2, 2, 0, 0, 是]], 是, finite_metric_is_complete_but_full_pair_audit_is_still_required)

Wave6第十層核對=(3, 是, 1/2, 是, [[0, 0, 0, 0, 是], [0, 1, 0, 1, 是], [0, 2, 2, 3, 是], [1, 0, 0, 1, 是], [1, 1, 0, 0, 是], [1, 2, 2, 2, 是], [2, 0, 2, 3, 是], [2, 1, 2, 2, 是], [2, 2, 0, 0, 是]], 是, finite_metric_is_complete_but_full_pair_audit_is_still_required)；依完整明示資料獨立重算；Picard orbit、unique fixed point與geometric tail bound使用exact arithmetic；q=1、非self-map、noncomplete或sampled-pairs不足；finite model不取代一般定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r01-contraction-mapping-theorem-0002/)

壓縮映射定理 · qf-mod47-contract-metric-qualification · candidate





## 3. 壓縮映射定理

完整metric、total self-map與forall-pairs q<1 contraction責任。操作=contract-metric-qualification；資料={"metric":[[0,3,9],[3,0,6],[9,6,0]],"mapping":[0,0,1],"q":[1,2]}。請依 [point_count, self_map, q, q_in_range, pair_inequality_rows, global_contraction, certificate] 欄序回答。

查看答案與解釋(3, 是, 1/2, 是, [[0, 0, 0, 0, 是], [0, 1, 0, 3/2, 是], [0, 2, 3, 9/2, 是], [1, 0, 0, 3/2, 是], [1, 1, 0, 0, 是], [1, 2, 3, 3, 是], [2, 0, 3, 9/2, 是], [2, 1, 3, 3, 是], [2, 2, 0, 0, 是]], 是, finite_metric_is_complete_but_full_pair_audit_is_still_required)

Wave6第十層核對=(3, 是, 1/2, 是, [[0, 0, 0, 0, 是], [0, 1, 0, 3/2, 是], [0, 2, 3, 9/2, 是], [1, 0, 0, 3/2, 是], [1, 1, 0, 0, 是], [1, 2, 3, 3, 是], [2, 0, 3, 9/2, 是], [2, 1, 3, 3, 是], [2, 2, 0, 0, 是]], 是, finite_metric_is_complete_but_full_pair_audit_is_still_required)；依完整明示資料獨立重算；Picard orbit、unique fixed point與geometric tail bound使用exact arithmetic；q=1、非self-map、noncomplete或sampled-pairs不足；finite model不取代一般定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r01-contraction-mapping-theorem-0003/)

壓縮映射定理 · qf-mod47-contract-metric-qualification · candidate





## 4. 壓縮映射定理

完整metric、total self-map與forall-pairs q<1 contraction責任。操作=contract-metric-qualification；資料={"metric":[[0,4,12],[4,0,8],[12,8,0]],"mapping":[0,0,1],"q":[1,2]}。請依 [point_count, self_map, q, q_in_range, pair_inequality_rows, global_contraction, certificate] 欄序回答。

查看答案與解釋(3, 是, 1/2, 是, [[0, 0, 0, 0, 是], [0, 1, 0, 2, 是], [0, 2, 4, 6, 是], [1, 0, 0, 2, 是], [1, 1, 0, 0, 是], [1, 2, 4, 4, 是], [2, 0, 4, 6, 是], [2, 1, 4, 4, 是], [2, 2, 0, 0, 是]], 是, finite_metric_is_complete_but_full_pair_audit_is_still_required)

Wave6第十層核對=(3, 是, 1/2, 是, [[0, 0, 0, 0, 是], [0, 1, 0, 2, 是], [0, 2, 4, 6, 是], [1, 0, 0, 2, 是], [1, 1, 0, 0, 是], [1, 2, 4, 4, 是], [2, 0, 4, 6, 是], [2, 1, 4, 4, 是], [2, 2, 0, 0, 是]], 是, finite_metric_is_complete_but_full_pair_audit_is_still_required)；依完整明示資料獨立重算；Picard orbit、unique fixed point與geometric tail bound使用exact arithmetic；q=1、非self-map、noncomplete或sampled-pairs不足；finite model不取代一般定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r01-contraction-mapping-theorem-0004/)

壓縮映射定理 · qf-mod47-contract-metric-qualification · candidate





## 5. 壓縮映射定理

完整metric、total self-map與forall-pairs q<1 contraction責任。操作=contract-metric-qualification；資料={"metric":[[0,5,15],[5,0,10],[15,10,0]],"mapping":[0,0,1],"q":[1,2]}。請依 [point_count, self_map, q, q_in_range, pair_inequality_rows, global_contraction, certificate] 欄序回答。

查看答案與解釋(3, 是, 1/2, 是, [[0, 0, 0, 0, 是], [0, 1, 0, 5/2, 是], [0, 2, 5, 15/2, 是], [1, 0, 0, 5/2, 是], [1, 1, 0, 0, 是], [1, 2, 5, 5, 是], [2, 0, 5, 15/2, 是], [2, 1, 5, 5, 是], [2, 2, 0, 0, 是]], 是, finite_metric_is_complete_but_full_pair_audit_is_still_required)

Wave6第十層核對=(3, 是, 1/2, 是, [[0, 0, 0, 0, 是], [0, 1, 0, 5/2, 是], [0, 2, 5, 15/2, 是], [1, 0, 0, 5/2, 是], [1, 1, 0, 0, 是], [1, 2, 5, 5, 是], [2, 0, 5, 15/2, 是], [2, 1, 5, 5, 是], [2, 2, 0, 0, 是]], 是, finite_metric_is_complete_but_full_pair_audit_is_still_required)；依完整明示資料獨立重算；Picard orbit、unique fixed point與geometric tail bound使用exact arithmetic；q=1、非self-map、noncomplete或sampled-pairs不足；finite model不取代一般定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r01-contraction-mapping-theorem-0005/)

壓縮映射定理 · qf-mod47-contract-metric-qualification · candidate





## 6. 壓縮映射定理

完整metric、total self-map與forall-pairs q<1 contraction責任。操作=contract-metric-qualification；資料={"metric":[[0,6,18],[6,0,12],[18,12,0]],"mapping":[0,0,1],"q":[1,2]}。請依 [point_count, self_map, q, q_in_range, pair_inequality_rows, global_contraction, certificate] 欄序回答。

查看答案與解釋(3, 是, 1/2, 是, [[0, 0, 0, 0, 是], [0, 1, 0, 3, 是], [0, 2, 6, 9, 是], [1, 0, 0, 3, 是], [1, 1, 0, 0, 是], [1, 2, 6, 6, 是], [2, 0, 6, 9, 是], [2, 1, 6, 6, 是], [2, 2, 0, 0, 是]], 是, finite_metric_is_complete_but_full_pair_audit_is_still_required)

Wave6第十層核對=(3, 是, 1/2, 是, [[0, 0, 0, 0, 是], [0, 1, 0, 3, 是], [0, 2, 6, 9, 是], [1, 0, 0, 3, 是], [1, 1, 0, 0, 是], [1, 2, 6, 6, 是], [2, 0, 6, 9, 是], [2, 1, 6, 6, 是], [2, 2, 0, 0, 是]], 是, finite_metric_is_complete_but_full_pair_audit_is_still_required)；依完整明示資料獨立重算；Picard orbit、unique fixed point與geometric tail bound使用exact arithmetic；q=1、非self-map、noncomplete或sampled-pairs不足；finite model不取代一般定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r01-contraction-mapping-theorem-0006/)

壓縮映射定理 · qf-mod47-contract-metric-qualification · candidate





## 7. 壓縮映射定理

完整metric、total self-map與forall-pairs q<1 contraction責任。操作=contract-metric-qualification；資料={"metric":[[0,7,21],[7,0,14],[21,14,0]],"mapping":[0,0,1],"q":[1,2]}。請依 [point_count, self_map, q, q_in_range, pair_inequality_rows, global_contraction, certificate] 欄序回答。

查看答案與解釋(3, 是, 1/2, 是, [[0, 0, 0, 0, 是], [0, 1, 0, 7/2, 是], [0, 2, 7, 21/2, 是], [1, 0, 0, 7/2, 是], [1, 1, 0, 0, 是], [1, 2, 7, 7, 是], [2, 0, 7, 21/2, 是], [2, 1, 7, 7, 是], [2, 2, 0, 0, 是]], 是, finite_metric_is_complete_but_full_pair_audit_is_still_required)

Wave6第十層核對=(3, 是, 1/2, 是, [[0, 0, 0, 0, 是], [0, 1, 0, 7/2, 是], [0, 2, 7, 21/2, 是], [1, 0, 0, 7/2, 是], [1, 1, 0, 0, 是], [1, 2, 7, 7, 是], [2, 0, 7, 21/2, 是], [2, 1, 7, 7, 是], [2, 2, 0, 0, 是]], 是, finite_metric_is_complete_but_full_pair_audit_is_still_required)；依完整明示資料獨立重算；Picard orbit、unique fixed point與geometric tail bound使用exact arithmetic；q=1、非self-map、noncomplete或sampled-pairs不足；finite model不取代一般定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r01-contraction-mapping-theorem-0007/)

壓縮映射定理 · qf-mod47-contract-metric-qualification · candidate





## 8. 壓縮映射定理

完整metric、total self-map與forall-pairs q<1 contraction責任。操作=contract-metric-qualification；資料={"metric":[[0,8,24],[8,0,16],[24,16,0]],"mapping":[0,0,1],"q":[1,2]}。請依 [point_count, self_map, q, q_in_range, pair_inequality_rows, global_contraction, certificate] 欄序回答。

查看答案與解釋(3, 是, 1/2, 是, [[0, 0, 0, 0, 是], [0, 1, 0, 4, 是], [0, 2, 8, 12, 是], [1, 0, 0, 4, 是], [1, 1, 0, 0, 是], [1, 2, 8, 8, 是], [2, 0, 8, 12, 是], [2, 1, 8, 8, 是], [2, 2, 0, 0, 是]], 是, finite_metric_is_complete_but_full_pair_audit_is_still_required)

Wave6第十層核對=(3, 是, 1/2, 是, [[0, 0, 0, 0, 是], [0, 1, 0, 4, 是], [0, 2, 8, 12, 是], [1, 0, 0, 4, 是], [1, 1, 0, 0, 是], [1, 2, 8, 8, 是], [2, 0, 8, 12, 是], [2, 1, 8, 8, 是], [2, 2, 0, 0, 是]], 是, finite_metric_is_complete_but_full_pair_audit_is_still_required)；依完整明示資料獨立重算；Picard orbit、unique fixed point與geometric tail bound使用exact arithmetic；q=1、非self-map、noncomplete或sampled-pairs不足；finite model不取代一般定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r01-contraction-mapping-theorem-0008/)

壓縮映射定理 · qf-mod47-contract-metric-qualification · candidate





## 9. 壓縮映射定理

完整metric、total self-map與forall-pairs q<1 contraction責任。操作=contract-metric-qualification；資料={"metric":[[0,9,27],[9,0,18],[27,18,0]],"mapping":[0,0,1],"q":[1,2]}。請依 [point_count, self_map, q, q_in_range, pair_inequality_rows, global_contraction, certificate] 欄序回答。

查看答案與解釋(3, 是, 1/2, 是, [[0, 0, 0, 0, 是], [0, 1, 0, 9/2, 是], [0, 2, 9, 27/2, 是], [1, 0, 0, 9/2, 是], [1, 1, 0, 0, 是], [1, 2, 9, 9, 是], [2, 0, 9, 27/2, 是], [2, 1, 9, 9, 是], [2, 2, 0, 0, 是]], 是, finite_metric_is_complete_but_full_pair_audit_is_still_required)

Wave6第十層核對=(3, 是, 1/2, 是, [[0, 0, 0, 0, 是], [0, 1, 0, 9/2, 是], [0, 2, 9, 27/2, 是], [1, 0, 0, 9/2, 是], [1, 1, 0, 0, 是], [1, 2, 9, 9, 是], [2, 0, 9, 27/2, 是], [2, 1, 9, 9, 是], [2, 2, 0, 0, 是]], 是, finite_metric_is_complete_but_full_pair_audit_is_still_required)；依完整明示資料獨立重算；Picard orbit、unique fixed point與geometric tail bound使用exact arithmetic；q=1、非self-map、noncomplete或sampled-pairs不足；finite model不取代一般定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r01-contraction-mapping-theorem-0009/)

壓縮映射定理 · qf-mod47-contract-metric-qualification · candidate





## 10. 壓縮映射定理

完整metric、total self-map與forall-pairs q<1 contraction責任。操作=contract-metric-qualification；資料={"metric":[[0,10,30],[10,0,20],[30,20,0]],"mapping":[0,0,1],"q":[1,2]}。請依 [point_count, self_map, q, q_in_range, pair_inequality_rows, global_contraction, certificate] 欄序回答。

查看答案與解釋(3, 是, 1/2, 是, [[0, 0, 0, 0, 是], [0, 1, 0, 5, 是], [0, 2, 10, 15, 是], [1, 0, 0, 5, 是], [1, 1, 0, 0, 是], [1, 2, 10, 10, 是], [2, 0, 10, 15, 是], [2, 1, 10, 10, 是], [2, 2, 0, 0, 是]], 是, finite_metric_is_complete_but_full_pair_audit_is_still_required)

Wave6第十層核對=(3, 是, 1/2, 是, [[0, 0, 0, 0, 是], [0, 1, 0, 5, 是], [0, 2, 10, 15, 是], [1, 0, 0, 5, 是], [1, 1, 0, 0, 是], [1, 2, 10, 10, 是], [2, 0, 10, 15, 是], [2, 1, 10, 10, 是], [2, 2, 0, 0, 是]], 是, finite_metric_is_complete_but_full_pair_audit_is_still_required)；依完整明示資料獨立重算；Picard orbit、unique fixed point與geometric tail bound使用exact arithmetic；q=1、非self-map、noncomplete或sampled-pairs不足；finite model不取代一般定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r01-contraction-mapping-theorem-0010/)

壓縮映射定理 · qf-mod47-contract-metric-qualification · candidate





## 11. 壓縮映射定理

完整metric、total self-map與forall-pairs q<1 contraction責任。操作=contract-metric-qualification；資料={"metric":[[0,11,33],[11,0,22],[33,22,0]],"mapping":[0,0,1],"q":[1,2]}。請依 [point_count, self_map, q, q_in_range, pair_inequality_rows, global_contraction, certificate] 欄序回答。

查看答案與解釋(3, 是, 1/2, 是, [[0, 0, 0, 0, 是], [0, 1, 0, 11/2, 是], [0, 2, 11, 33/2, 是], [1, 0, 0, 11/2, 是], [1, 1, 0, 0, 是], [1, 2, 11, 11, 是], [2, 0, 11, 33/2, 是], [2, 1, 11, 11, 是], [2, 2, 0, 0, 是]], 是, finite_metric_is_complete_but_full_pair_audit_is_still_required)

Wave6第十層核對=(3, 是, 1/2, 是, [[0, 0, 0, 0, 是], [0, 1, 0, 11/2, 是], [0, 2, 11, 33/2, 是], [1, 0, 0, 11/2, 是], [1, 1, 0, 0, 是], [1, 2, 11, 11, 是], [2, 0, 11, 33/2, 是], [2, 1, 11, 11, 是], [2, 2, 0, 0, 是]], 是, finite_metric_is_complete_but_full_pair_audit_is_still_required)；依完整明示資料獨立重算；Picard orbit、unique fixed point與geometric tail bound使用exact arithmetic；q=1、非self-map、noncomplete或sampled-pairs不足；finite model不取代一般定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r01-contraction-mapping-theorem-0011/)

壓縮映射定理 · qf-mod47-contract-metric-qualification · candidate





## 12. 壓縮映射定理

完整metric、total self-map與forall-pairs q<1 contraction責任。操作=contract-metric-qualification；資料={"metric":[[0,12,36],[12,0,24],[36,24,0]],"mapping":[0,0,1],"q":[1,2]}。請依 [point_count, self_map, q, q_in_range, pair_inequality_rows, global_contraction, certificate] 欄序回答。

查看答案與解釋(3, 是, 1/2, 是, [[0, 0, 0, 0, 是], [0, 1, 0, 6, 是], [0, 2, 12, 18, 是], [1, 0, 0, 6, 是], [1, 1, 0, 0, 是], [1, 2, 12, 12, 是], [2, 0, 12, 18, 是], [2, 1, 12, 12, 是], [2, 2, 0, 0, 是]], 是, finite_metric_is_complete_but_full_pair_audit_is_still_required)

Wave6第十層核對=(3, 是, 1/2, 是, [[0, 0, 0, 0, 是], [0, 1, 0, 6, 是], [0, 2, 12, 18, 是], [1, 0, 0, 6, 是], [1, 1, 0, 0, 是], [1, 2, 12, 12, 是], [2, 0, 12, 18, 是], [2, 1, 12, 12, 是], [2, 2, 0, 0, 是]], 是, finite_metric_is_complete_but_full_pair_audit_is_still_required)；依完整明示資料獨立重算；Picard orbit、unique fixed point與geometric tail bound使用exact arithmetic；q=1、非self-map、noncomplete或sampled-pairs不足；finite model不取代一般定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r01-contraction-mapping-theorem-0012/)

壓縮映射定理 · qf-mod47-contract-metric-qualification · candidate





## 13. 壓縮映射定理

完整metric、total self-map與forall-pairs q<1 contraction責任。操作=contract-metric-qualification；資料={"metric":[[0,13,39],[13,0,26],[39,26,0]],"mapping":[0,0,1],"q":[1,2]}。請依 [point_count, self_map, q, q_in_range, pair_inequality_rows, global_contraction, certificate] 欄序回答。

查看答案與解釋(3, 是, 1/2, 是, [[0, 0, 0, 0, 是], [0, 1, 0, 13/2, 是], [0, 2, 13, 39/2, 是], [1, 0, 0, 13/2, 是], [1, 1, 0, 0, 是], [1, 2, 13, 13, 是], [2, 0, 13, 39/2, 是], [2, 1, 13, 13, 是], [2, 2, 0, 0, 是]], 是, finite_metric_is_complete_but_full_pair_audit_is_still_required)

Wave6第十層核對=(3, 是, 1/2, 是, [[0, 0, 0, 0, 是], [0, 1, 0, 13/2, 是], [0, 2, 13, 39/2, 是], [1, 0, 0, 13/2, 是], [1, 1, 0, 0, 是], [1, 2, 13, 13, 是], [2, 0, 13, 39/2, 是], [2, 1, 13, 13, 是], [2, 2, 0, 0, 是]], 是, finite_metric_is_complete_but_full_pair_audit_is_still_required)；依完整明示資料獨立重算；Picard orbit、unique fixed point與geometric tail bound使用exact arithmetic；q=1、非self-map、noncomplete或sampled-pairs不足；finite model不取代一般定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r01-contraction-mapping-theorem-0013/)

壓縮映射定理 · qf-mod47-contract-metric-qualification · candidate





## 14. 壓縮映射定理

完整metric、total self-map與forall-pairs q<1 contraction責任。操作=contract-metric-qualification；資料={"metric":[[0,14,42],[14,0,28],[42,28,0]],"mapping":[0,0,1],"q":[1,2]}。請依 [point_count, self_map, q, q_in_range, pair_inequality_rows, global_contraction, certificate] 欄序回答。

查看答案與解釋(3, 是, 1/2, 是, [[0, 0, 0, 0, 是], [0, 1, 0, 7, 是], [0, 2, 14, 21, 是], [1, 0, 0, 7, 是], [1, 1, 0, 0, 是], [1, 2, 14, 14, 是], [2, 0, 14, 21, 是], [2, 1, 14, 14, 是], [2, 2, 0, 0, 是]], 是, finite_metric_is_complete_but_full_pair_audit_is_still_required)

Wave6第十層核對=(3, 是, 1/2, 是, [[0, 0, 0, 0, 是], [0, 1, 0, 7, 是], [0, 2, 14, 21, 是], [1, 0, 0, 7, 是], [1, 1, 0, 0, 是], [1, 2, 14, 14, 是], [2, 0, 14, 21, 是], [2, 1, 14, 14, 是], [2, 2, 0, 0, 是]], 是, finite_metric_is_complete_but_full_pair_audit_is_still_required)；依完整明示資料獨立重算；Picard orbit、unique fixed point與geometric tail bound使用exact arithmetic；q=1、非self-map、noncomplete或sampled-pairs不足；finite model不取代一般定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r01-contraction-mapping-theorem-0014/)

壓縮映射定理 · qf-mod47-contract-metric-qualification · candidate





## 15. 壓縮映射定理

完整metric、total self-map與forall-pairs q<1 contraction責任。操作=contract-metric-qualification；資料={"metric":[[0,15,45],[15,0,30],[45,30,0]],"mapping":[0,0,1],"q":[1,2]}。請依 [point_count, self_map, q, q_in_range, pair_inequality_rows, global_contraction, certificate] 欄序回答。

查看答案與解釋(3, 是, 1/2, 是, [[0, 0, 0, 0, 是], [0, 1, 0, 15/2, 是], [0, 2, 15, 45/2, 是], [1, 0, 0, 15/2, 是], [1, 1, 0, 0, 是], [1, 2, 15, 15, 是], [2, 0, 15, 45/2, 是], [2, 1, 15, 15, 是], [2, 2, 0, 0, 是]], 是, finite_metric_is_complete_but_full_pair_audit_is_still_required)

Wave6第十層核對=(3, 是, 1/2, 是, [[0, 0, 0, 0, 是], [0, 1, 0, 15/2, 是], [0, 2, 15, 45/2, 是], [1, 0, 0, 15/2, 是], [1, 1, 0, 0, 是], [1, 2, 15, 15, 是], [2, 0, 15, 45/2, 是], [2, 1, 15, 15, 是], [2, 2, 0, 0, 是]], 是, finite_metric_is_complete_but_full_pair_audit_is_still_required)；依完整明示資料獨立重算；Picard orbit、unique fixed point與geometric tail bound使用exact arithmetic；q=1、非self-map、noncomplete或sampled-pairs不足；finite model不取代一般定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r01-contraction-mapping-theorem-0015/)

壓縮映射定理 · qf-mod47-contract-metric-qualification · candidate





## 16. 壓縮映射定理

完整metric、total self-map與forall-pairs q<1 contraction責任。操作=contract-metric-qualification；資料={"metric":[[0,16,48],[16,0,32],[48,32,0]],"mapping":[0,0,1],"q":[1,2]}。請依 [point_count, self_map, q, q_in_range, pair_inequality_rows, global_contraction, certificate] 欄序回答。

查看答案與解釋(3, 是, 1/2, 是, [[0, 0, 0, 0, 是], [0, 1, 0, 8, 是], [0, 2, 16, 24, 是], [1, 0, 0, 8, 是], [1, 1, 0, 0, 是], [1, 2, 16, 16, 是], [2, 0, 16, 24, 是], [2, 1, 16, 16, 是], [2, 2, 0, 0, 是]], 是, finite_metric_is_complete_but_full_pair_audit_is_still_required)

Wave6第十層核對=(3, 是, 1/2, 是, [[0, 0, 0, 0, 是], [0, 1, 0, 8, 是], [0, 2, 16, 24, 是], [1, 0, 0, 8, 是], [1, 1, 0, 0, 是], [1, 2, 16, 16, 是], [2, 0, 16, 24, 是], [2, 1, 16, 16, 是], [2, 2, 0, 0, 是]], 是, finite_metric_is_complete_but_full_pair_audit_is_still_required)；依完整明示資料獨立重算；Picard orbit、unique fixed point與geometric tail bound使用exact arithmetic；q=1、非self-map、noncomplete或sampled-pairs不足；finite model不取代一般定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r01-contraction-mapping-theorem-0016/)

壓縮映射定理 · qf-mod47-contract-metric-qualification · candidate





## 17. 壓縮映射定理

完整metric、total self-map與forall-pairs q<1 contraction責任。操作=contract-metric-qualification；資料={"metric":[[0,17,51],[17,0,34],[51,34,0]],"mapping":[0,0,1],"q":[1,2]}。請依 [point_count, self_map, q, q_in_range, pair_inequality_rows, global_contraction, certificate] 欄序回答。

查看答案與解釋(3, 是, 1/2, 是, [[0, 0, 0, 0, 是], [0, 1, 0, 17/2, 是], [0, 2, 17, 51/2, 是], [1, 0, 0, 17/2, 是], [1, 1, 0, 0, 是], [1, 2, 17, 17, 是], [2, 0, 17, 51/2, 是], [2, 1, 17, 17, 是], [2, 2, 0, 0, 是]], 是, finite_metric_is_complete_but_full_pair_audit_is_still_required)

Wave6第十層核對=(3, 是, 1/2, 是, [[0, 0, 0, 0, 是], [0, 1, 0, 17/2, 是], [0, 2, 17, 51/2, 是], [1, 0, 0, 17/2, 是], [1, 1, 0, 0, 是], [1, 2, 17, 17, 是], [2, 0, 17, 51/2, 是], [2, 1, 17, 17, 是], [2, 2, 0, 0, 是]], 是, finite_metric_is_complete_but_full_pair_audit_is_still_required)；依完整明示資料獨立重算；Picard orbit、unique fixed point與geometric tail bound使用exact arithmetic；q=1、非self-map、noncomplete或sampled-pairs不足；finite model不取代一般定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r01-contraction-mapping-theorem-0017/)

壓縮映射定理 · qf-mod47-contract-metric-qualification · candidate





## 18. 壓縮映射定理

完整metric、total self-map與forall-pairs q<1 contraction責任。操作=contract-metric-qualification；資料={"metric":[[0,18,54],[18,0,36],[54,36,0]],"mapping":[0,0,1],"q":[1,2]}。請依 [point_count, self_map, q, q_in_range, pair_inequality_rows, global_contraction, certificate] 欄序回答。

查看答案與解釋(3, 是, 1/2, 是, [[0, 0, 0, 0, 是], [0, 1, 0, 9, 是], [0, 2, 18, 27, 是], [1, 0, 0, 9, 是], [1, 1, 0, 0, 是], [1, 2, 18, 18, 是], [2, 0, 18, 27, 是], [2, 1, 18, 18, 是], [2, 2, 0, 0, 是]], 是, finite_metric_is_complete_but_full_pair_audit_is_still_required)

Wave6第十層核對=(3, 是, 1/2, 是, [[0, 0, 0, 0, 是], [0, 1, 0, 9, 是], [0, 2, 18, 27, 是], [1, 0, 0, 9, 是], [1, 1, 0, 0, 是], [1, 2, 18, 18, 是], [2, 0, 18, 27, 是], [2, 1, 18, 18, 是], [2, 2, 0, 0, 是]], 是, finite_metric_is_complete_but_full_pair_audit_is_still_required)；依完整明示資料獨立重算；Picard orbit、unique fixed point與geometric tail bound使用exact arithmetic；q=1、非self-map、noncomplete或sampled-pairs不足；finite model不取代一般定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r01-contraction-mapping-theorem-0018/)

壓縮映射定理 · qf-mod47-contract-metric-qualification · candidate





## 19. 壓縮映射定理

完整metric、total self-map與forall-pairs q<1 contraction責任。操作=contract-metric-qualification；資料={"metric":[[0,19,57],[19,0,38],[57,38,0]],"mapping":[0,0,1],"q":[1,2]}。請依 [point_count, self_map, q, q_in_range, pair_inequality_rows, global_contraction, certificate] 欄序回答。

查看答案與解釋(3, 是, 1/2, 是, [[0, 0, 0, 0, 是], [0, 1, 0, 19/2, 是], [0, 2, 19, 57/2, 是], [1, 0, 0, 19/2, 是], [1, 1, 0, 0, 是], [1, 2, 19, 19, 是], [2, 0, 19, 57/2, 是], [2, 1, 19, 19, 是], [2, 2, 0, 0, 是]], 是, finite_metric_is_complete_but_full_pair_audit_is_still_required)

Wave6第十層核對=(3, 是, 1/2, 是, [[0, 0, 0, 0, 是], [0, 1, 0, 19/2, 是], [0, 2, 19, 57/2, 是], [1, 0, 0, 19/2, 是], [1, 1, 0, 0, 是], [1, 2, 19, 19, 是], [2, 0, 19, 57/2, 是], [2, 1, 19, 19, 是], [2, 2, 0, 0, 是]], 是, finite_metric_is_complete_but_full_pair_audit_is_still_required)；依完整明示資料獨立重算；Picard orbit、unique fixed point與geometric tail bound使用exact arithmetic；q=1、非self-map、noncomplete或sampled-pairs不足；finite model不取代一般定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r01-contraction-mapping-theorem-0019/)

壓縮映射定理 · qf-mod47-contract-metric-qualification · candidate





## 20. 壓縮映射定理

完整metric、total self-map與forall-pairs q<1 contraction責任。操作=contract-metric-qualification；資料={"metric":[[0,20,60],[20,0,40],[60,40,0]],"mapping":[0,0,1],"q":[1,2]}。請依 [point_count, self_map, q, q_in_range, pair_inequality_rows, global_contraction, certificate] 欄序回答。

查看答案與解釋(3, 是, 1/2, 是, [[0, 0, 0, 0, 是], [0, 1, 0, 10, 是], [0, 2, 20, 30, 是], [1, 0, 0, 10, 是], [1, 1, 0, 0, 是], [1, 2, 20, 20, 是], [2, 0, 20, 30, 是], [2, 1, 20, 20, 是], [2, 2, 0, 0, 是]], 是, finite_metric_is_complete_but_full_pair_audit_is_still_required)

Wave6第十層核對=(3, 是, 1/2, 是, [[0, 0, 0, 0, 是], [0, 1, 0, 10, 是], [0, 2, 20, 30, 是], [1, 0, 0, 10, 是], [1, 1, 0, 0, 是], [1, 2, 20, 20, 是], [2, 0, 20, 30, 是], [2, 1, 20, 20, 是], [2, 2, 0, 0, 是]], 是, finite_metric_is_complete_but_full_pair_audit_is_still_required)；依完整明示資料獨立重算；Picard orbit、unique fixed point與geometric tail bound使用exact arithmetic；q=1、非self-map、noncomplete或sampled-pairs不足；finite model不取代一般定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r01-contraction-mapping-theorem-0020/)

壓縮映射定理 · qf-mod47-contract-metric-qualification · candidate





## 21. 壓縮映射定理

完整metric、total self-map與forall-pairs q<1 contraction責任。操作=contract-metric-qualification；資料={"metric":[[0,21,63],[21,0,42],[63,42,0]],"mapping":[0,0,1],"q":[1,2]}。請依 [point_count, self_map, q, q_in_range, pair_inequality_rows, global_contraction, certificate] 欄序回答。

查看答案與解釋(3, 是, 1/2, 是, [[0, 0, 0, 0, 是], [0, 1, 0, 21/2, 是], [0, 2, 21, 63/2, 是], [1, 0, 0, 21/2, 是], [1, 1, 0, 0, 是], [1, 2, 21, 21, 是], [2, 0, 21, 63/2, 是], [2, 1, 21, 21, 是], [2, 2, 0, 0, 是]], 是, finite_metric_is_complete_but_full_pair_audit_is_still_required)

Wave6第十層核對=(3, 是, 1/2, 是, [[0, 0, 0, 0, 是], [0, 1, 0, 21/2, 是], [0, 2, 21, 63/2, 是], [1, 0, 0, 21/2, 是], [1, 1, 0, 0, 是], [1, 2, 21, 21, 是], [2, 0, 21, 63/2, 是], [2, 1, 21, 21, 是], [2, 2, 0, 0, 是]], 是, finite_metric_is_complete_but_full_pair_audit_is_still_required)；依完整明示資料獨立重算；Picard orbit、unique fixed point與geometric tail bound使用exact arithmetic；q=1、非self-map、noncomplete或sampled-pairs不足；finite model不取代一般定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r01-contraction-mapping-theorem-0021/)

壓縮映射定理 · qf-mod47-contract-metric-qualification · candidate





## 22. 壓縮映射定理

完整metric、total self-map與forall-pairs q<1 contraction責任。操作=contract-metric-qualification；資料={"metric":[[0,22,66],[22,0,44],[66,44,0]],"mapping":[0,0,1],"q":[1,2]}。請依 [point_count, self_map, q, q_in_range, pair_inequality_rows, global_contraction, certificate] 欄序回答。

查看答案與解釋(3, 是, 1/2, 是, [[0, 0, 0, 0, 是], [0, 1, 0, 11, 是], [0, 2, 22, 33, 是], [1, 0, 0, 11, 是], [1, 1, 0, 0, 是], [1, 2, 22, 22, 是], [2, 0, 22, 33, 是], [2, 1, 22, 22, 是], [2, 2, 0, 0, 是]], 是, finite_metric_is_complete_but_full_pair_audit_is_still_required)

Wave6第十層核對=(3, 是, 1/2, 是, [[0, 0, 0, 0, 是], [0, 1, 0, 11, 是], [0, 2, 22, 33, 是], [1, 0, 0, 11, 是], [1, 1, 0, 0, 是], [1, 2, 22, 22, 是], [2, 0, 22, 33, 是], [2, 1, 22, 22, 是], [2, 2, 0, 0, 是]], 是, finite_metric_is_complete_but_full_pair_audit_is_still_required)；依完整明示資料獨立重算；Picard orbit、unique fixed point與geometric tail bound使用exact arithmetic；q=1、非self-map、noncomplete或sampled-pairs不足；finite model不取代一般定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r01-contraction-mapping-theorem-0022/)

壓縮映射定理 · qf-mod47-contract-metric-qualification · candidate





## 23. 壓縮映射定理

完整metric、total self-map與forall-pairs q<1 contraction責任。操作=contract-metric-qualification；資料={"metric":[[0,23,69],[23,0,46],[69,46,0]],"mapping":[0,0,1],"q":[1,2]}。請依 [point_count, self_map, q, q_in_range, pair_inequality_rows, global_contraction, certificate] 欄序回答。

查看答案與解釋(3, 是, 1/2, 是, [[0, 0, 0, 0, 是], [0, 1, 0, 23/2, 是], [0, 2, 23, 69/2, 是], [1, 0, 0, 23/2, 是], [1, 1, 0, 0, 是], [1, 2, 23, 23, 是], [2, 0, 23, 69/2, 是], [2, 1, 23, 23, 是], [2, 2, 0, 0, 是]], 是, finite_metric_is_complete_but_full_pair_audit_is_still_required)

Wave6第十層核對=(3, 是, 1/2, 是, [[0, 0, 0, 0, 是], [0, 1, 0, 23/2, 是], [0, 2, 23, 69/2, 是], [1, 0, 0, 23/2, 是], [1, 1, 0, 0, 是], [1, 2, 23, 23, 是], [2, 0, 23, 69/2, 是], [2, 1, 23, 23, 是], [2, 2, 0, 0, 是]], 是, finite_metric_is_complete_but_full_pair_audit_is_still_required)；依完整明示資料獨立重算；Picard orbit、unique fixed point與geometric tail bound使用exact arithmetic；q=1、非self-map、noncomplete或sampled-pairs不足；finite model不取代一般定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r01-contraction-mapping-theorem-0023/)

壓縮映射定理 · qf-mod47-contract-metric-qualification · candidate





## 24. 壓縮映射定理

完整metric、total self-map與forall-pairs q<1 contraction責任。操作=contract-metric-qualification；資料={"metric":[[0,24,72],[24,0,48],[72,48,0]],"mapping":[0,0,1],"q":[1,2]}。請依 [point_count, self_map, q, q_in_range, pair_inequality_rows, global_contraction, certificate] 欄序回答。

查看答案與解釋(3, 是, 1/2, 是, [[0, 0, 0, 0, 是], [0, 1, 0, 12, 是], [0, 2, 24, 36, 是], [1, 0, 0, 12, 是], [1, 1, 0, 0, 是], [1, 2, 24, 24, 是], [2, 0, 24, 36, 是], [2, 1, 24, 24, 是], [2, 2, 0, 0, 是]], 是, finite_metric_is_complete_but_full_pair_audit_is_still_required)

Wave6第十層核對=(3, 是, 1/2, 是, [[0, 0, 0, 0, 是], [0, 1, 0, 12, 是], [0, 2, 24, 36, 是], [1, 0, 0, 12, 是], [1, 1, 0, 0, 是], [1, 2, 24, 24, 是], [2, 0, 24, 36, 是], [2, 1, 24, 24, 是], [2, 2, 0, 0, 是]], 是, finite_metric_is_complete_but_full_pair_audit_is_still_required)；依完整明示資料獨立重算；Picard orbit、unique fixed point與geometric tail bound使用exact arithmetic；q=1、非self-map、noncomplete或sampled-pairs不足；finite model不取代一般定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r01-contraction-mapping-theorem-0024/)

壓縮映射定理 · qf-mod47-contract-metric-qualification · candidate





## 25. 壓縮映射定理

完整metric、total self-map與forall-pairs q<1 contraction責任。操作=contract-metric-qualification；資料={"metric":[[0,25,75],[25,0,50],[75,50,0]],"mapping":[0,0,1],"q":[1,2]}。請依 [point_count, self_map, q, q_in_range, pair_inequality_rows, global_contraction, certificate] 欄序回答。

查看答案與解釋(3, 是, 1/2, 是, [[0, 0, 0, 0, 是], [0, 1, 0, 25/2, 是], [0, 2, 25, 75/2, 是], [1, 0, 0, 25/2, 是], [1, 1, 0, 0, 是], [1, 2, 25, 25, 是], [2, 0, 25, 75/2, 是], [2, 1, 25, 25, 是], [2, 2, 0, 0, 是]], 是, finite_metric_is_complete_but_full_pair_audit_is_still_required)

Wave6第十層核對=(3, 是, 1/2, 是, [[0, 0, 0, 0, 是], [0, 1, 0, 25/2, 是], [0, 2, 25, 75/2, 是], [1, 0, 0, 25/2, 是], [1, 1, 0, 0, 是], [1, 2, 25, 25, 是], [2, 0, 25, 75/2, 是], [2, 1, 25, 25, 是], [2, 2, 0, 0, 是]], 是, finite_metric_is_complete_but_full_pair_audit_is_still_required)；依完整明示資料獨立重算；Picard orbit、unique fixed point與geometric tail bound使用exact arithmetic；q=1、非self-map、noncomplete或sampled-pairs不足；finite model不取代一般定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r01-contraction-mapping-theorem-0025/)

壓縮映射定理 · qf-mod47-contract-metric-qualification · candidate





## 26. 壓縮映射定理

完整metric、total self-map與forall-pairs q<1 contraction責任。操作=contract-picard-orbit；資料={"metric":[[0,1,3],[1,0,2],[3,2,0]],"mapping":[0,0,1],"q":[1,2],"start":2,"steps":2}。請依 [start, steps, orbit, fixed_point, distances_to_fixed_point, certificate] 欄序回答。

查看答案與解釋(2, 2, [2, 1, 0], 0, [3, 1, 0], exact_Picard_orbit)

Wave6第十層核對=(2, 2, [2, 1, 0], 0, [3, 1, 0], exact_Picard_orbit)；依完整明示資料獨立重算；Picard orbit、unique fixed point與geometric tail bound使用exact arithmetic；q=1、非self-map、noncomplete或sampled-pairs不足；finite model不取代一般定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r01-contraction-mapping-theorem-0026/)

壓縮映射定理 · qf-mod47-contract-picard-orbit · candidate





## 27. 壓縮映射定理

完整metric、total self-map與forall-pairs q<1 contraction責任。操作=contract-picard-orbit；資料={"metric":[[0,2,6],[2,0,4],[6,4,0]],"mapping":[0,0,1],"q":[1,2],"start":2,"steps":3}。請依 [start, steps, orbit, fixed_point, distances_to_fixed_point, certificate] 欄序回答。

查看答案與解釋(2, 3, [2, 1, 0, 0], 0, [6, 2, 0, 0], exact_Picard_orbit)

Wave6第十層核對=(2, 3, [2, 1, 0, 0], 0, [6, 2, 0, 0], exact_Picard_orbit)；依完整明示資料獨立重算；Picard orbit、unique fixed point與geometric tail bound使用exact arithmetic；q=1、非self-map、noncomplete或sampled-pairs不足；finite model不取代一般定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r01-contraction-mapping-theorem-0027/)

壓縮映射定理 · qf-mod47-contract-picard-orbit · candidate





## 28. 壓縮映射定理

完整metric、total self-map與forall-pairs q<1 contraction責任。操作=contract-picard-orbit；資料={"metric":[[0,3,9],[3,0,6],[9,6,0]],"mapping":[0,0,1],"q":[1,2],"start":2,"steps":4}。請依 [start, steps, orbit, fixed_point, distances_to_fixed_point, certificate] 欄序回答。

查看答案與解釋(2, 4, [2, 1, 0, 0, 0], 0, [9, 3, 0, 0, 0], exact_Picard_orbit)

Wave6第十層核對=(2, 4, [2, 1, 0, 0, 0], 0, [9, 3, 0, 0, 0], exact_Picard_orbit)；依完整明示資料獨立重算；Picard orbit、unique fixed point與geometric tail bound使用exact arithmetic；q=1、非self-map、noncomplete或sampled-pairs不足；finite model不取代一般定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r01-contraction-mapping-theorem-0028/)

壓縮映射定理 · qf-mod47-contract-picard-orbit · candidate





## 29. 壓縮映射定理

完整metric、total self-map與forall-pairs q<1 contraction責任。操作=contract-picard-orbit；資料={"metric":[[0,4,12],[4,0,8],[12,8,0]],"mapping":[0,0,1],"q":[1,2],"start":2,"steps":5}。請依 [start, steps, orbit, fixed_point, distances_to_fixed_point, certificate] 欄序回答。

查看答案與解釋(2, 5, [2, 1, 0, 0, 0, 0], 0, [12, 4, 0, 0, 0, 0], exact_Picard_orbit)

Wave6第十層核對=(2, 5, [2, 1, 0, 0, 0, 0], 0, [12, 4, 0, 0, 0, 0], exact_Picard_orbit)；依完整明示資料獨立重算；Picard orbit、unique fixed point與geometric tail bound使用exact arithmetic；q=1、非self-map、noncomplete或sampled-pairs不足；finite model不取代一般定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r01-contraction-mapping-theorem-0029/)

壓縮映射定理 · qf-mod47-contract-picard-orbit · candidate





## 30. 壓縮映射定理

完整metric、total self-map與forall-pairs q<1 contraction責任。操作=contract-picard-orbit；資料={"metric":[[0,5,15],[5,0,10],[15,10,0]],"mapping":[0,0,1],"q":[1,2],"start":2,"steps":6}。請依 [start, steps, orbit, fixed_point, distances_to_fixed_point, certificate] 欄序回答。

查看答案與解釋(2, 6, [2, 1, 0, 0, 0, 0, 0], 0, [15, 5, 0, 0, 0, 0, 0], exact_Picard_orbit)

Wave6第十層核對=(2, 6, [2, 1, 0, 0, 0, 0, 0], 0, [15, 5, 0, 0, 0, 0, 0], exact_Picard_orbit)；依完整明示資料獨立重算；Picard orbit、unique fixed point與geometric tail bound使用exact arithmetic；q=1、非self-map、noncomplete或sampled-pairs不足；finite model不取代一般定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r01-contraction-mapping-theorem-0030/)

壓縮映射定理 · qf-mod47-contract-picard-orbit · candidate





## 31. 壓縮映射定理

完整metric、total self-map與forall-pairs q<1 contraction責任。操作=contract-picard-orbit；資料={"metric":[[0,6,18],[6,0,12],[18,12,0]],"mapping":[0,0,1],"q":[1,2],"start":2,"steps":2}。請依 [start, steps, orbit, fixed_point, distances_to_fixed_point, certificate] 欄序回答。

查看答案與解釋(2, 2, [2, 1, 0], 0, [18, 6, 0], exact_Picard_orbit)

Wave6第十層核對=(2, 2, [2, 1, 0], 0, [18, 6, 0], exact_Picard_orbit)；依完整明示資料獨立重算；Picard orbit、unique fixed point與geometric tail bound使用exact arithmetic；q=1、非self-map、noncomplete或sampled-pairs不足；finite model不取代一般定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r01-contraction-mapping-theorem-0031/)

壓縮映射定理 · qf-mod47-contract-picard-orbit · candidate





## 32. 壓縮映射定理

完整metric、total self-map與forall-pairs q<1 contraction責任。操作=contract-picard-orbit；資料={"metric":[[0,7,21],[7,0,14],[21,14,0]],"mapping":[0,0,1],"q":[1,2],"start":2,"steps":3}。請依 [start, steps, orbit, fixed_point, distances_to_fixed_point, certificate] 欄序回答。

查看答案與解釋(2, 3, [2, 1, 0, 0], 0, [21, 7, 0, 0], exact_Picard_orbit)

Wave6第十層核對=(2, 3, [2, 1, 0, 0], 0, [21, 7, 0, 0], exact_Picard_orbit)；依完整明示資料獨立重算；Picard orbit、unique fixed point與geometric tail bound使用exact arithmetic；q=1、非self-map、noncomplete或sampled-pairs不足；finite model不取代一般定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r01-contraction-mapping-theorem-0032/)

壓縮映射定理 · qf-mod47-contract-picard-orbit · candidate





## 33. 壓縮映射定理

完整metric、total self-map與forall-pairs q<1 contraction責任。操作=contract-picard-orbit；資料={"metric":[[0,8,24],[8,0,16],[24,16,0]],"mapping":[0,0,1],"q":[1,2],"start":2,"steps":4}。請依 [start, steps, orbit, fixed_point, distances_to_fixed_point, certificate] 欄序回答。

查看答案與解釋(2, 4, [2, 1, 0, 0, 0], 0, [24, 8, 0, 0, 0], exact_Picard_orbit)

Wave6第十層核對=(2, 4, [2, 1, 0, 0, 0], 0, [24, 8, 0, 0, 0], exact_Picard_orbit)；依完整明示資料獨立重算；Picard orbit、unique fixed point與geometric tail bound使用exact arithmetic；q=1、非self-map、noncomplete或sampled-pairs不足；finite model不取代一般定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r01-contraction-mapping-theorem-0033/)

壓縮映射定理 · qf-mod47-contract-picard-orbit · candidate





## 34. 壓縮映射定理

完整metric、total self-map與forall-pairs q<1 contraction責任。操作=contract-picard-orbit；資料={"metric":[[0,9,27],[9,0,18],[27,18,0]],"mapping":[0,0,1],"q":[1,2],"start":2,"steps":5}。請依 [start, steps, orbit, fixed_point, distances_to_fixed_point, certificate] 欄序回答。

查看答案與解釋(2, 5, [2, 1, 0, 0, 0, 0], 0, [27, 9, 0, 0, 0, 0], exact_Picard_orbit)

Wave6第十層核對=(2, 5, [2, 1, 0, 0, 0, 0], 0, [27, 9, 0, 0, 0, 0], exact_Picard_orbit)；依完整明示資料獨立重算；Picard orbit、unique fixed point與geometric tail bound使用exact arithmetic；q=1、非self-map、noncomplete或sampled-pairs不足；finite model不取代一般定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r01-contraction-mapping-theorem-0034/)

壓縮映射定理 · qf-mod47-contract-picard-orbit · candidate





## 35. 壓縮映射定理

完整metric、total self-map與forall-pairs q<1 contraction責任。操作=contract-picard-orbit；資料={"metric":[[0,10,30],[10,0,20],[30,20,0]],"mapping":[0,0,1],"q":[1,2],"start":2,"steps":6}。請依 [start, steps, orbit, fixed_point, distances_to_fixed_point, certificate] 欄序回答。

查看答案與解釋(2, 6, [2, 1, 0, 0, 0, 0, 0], 0, [30, 10, 0, 0, 0, 0, 0], exact_Picard_orbit)

Wave6第十層核對=(2, 6, [2, 1, 0, 0, 0, 0, 0], 0, [30, 10, 0, 0, 0, 0, 0], exact_Picard_orbit)；依完整明示資料獨立重算；Picard orbit、unique fixed point與geometric tail bound使用exact arithmetic；q=1、非self-map、noncomplete或sampled-pairs不足；finite model不取代一般定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r01-contraction-mapping-theorem-0035/)

壓縮映射定理 · qf-mod47-contract-picard-orbit · candidate





## 36. 壓縮映射定理

完整metric、total self-map與forall-pairs q<1 contraction責任。操作=contract-picard-orbit；資料={"metric":[[0,11,33],[11,0,22],[33,22,0]],"mapping":[0,0,1],"q":[1,2],"start":2,"steps":2}。請依 [start, steps, orbit, fixed_point, distances_to_fixed_point, certificate] 欄序回答。

查看答案與解釋(2, 2, [2, 1, 0], 0, [33, 11, 0], exact_Picard_orbit)

Wave6第十層核對=(2, 2, [2, 1, 0], 0, [33, 11, 0], exact_Picard_orbit)；依完整明示資料獨立重算；Picard orbit、unique fixed point與geometric tail bound使用exact arithmetic；q=1、非self-map、noncomplete或sampled-pairs不足；finite model不取代一般定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r01-contraction-mapping-theorem-0036/)

壓縮映射定理 · qf-mod47-contract-picard-orbit · candidate





## 37. 壓縮映射定理

完整metric、total self-map與forall-pairs q<1 contraction責任。操作=contract-picard-orbit；資料={"metric":[[0,12,36],[12,0,24],[36,24,0]],"mapping":[0,0,1],"q":[1,2],"start":2,"steps":3}。請依 [start, steps, orbit, fixed_point, distances_to_fixed_point, certificate] 欄序回答。

查看答案與解釋(2, 3, [2, 1, 0, 0], 0, [36, 12, 0, 0], exact_Picard_orbit)

Wave6第十層核對=(2, 3, [2, 1, 0, 0], 0, [36, 12, 0, 0], exact_Picard_orbit)；依完整明示資料獨立重算；Picard orbit、unique fixed point與geometric tail bound使用exact arithmetic；q=1、非self-map、noncomplete或sampled-pairs不足；finite model不取代一般定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r01-contraction-mapping-theorem-0037/)

壓縮映射定理 · qf-mod47-contract-picard-orbit · candidate





## 38. 壓縮映射定理

完整metric、total self-map與forall-pairs q<1 contraction責任。操作=contract-picard-orbit；資料={"metric":[[0,13,39],[13,0,26],[39,26,0]],"mapping":[0,0,1],"q":[1,2],"start":2,"steps":4}。請依 [start, steps, orbit, fixed_point, distances_to_fixed_point, certificate] 欄序回答。

查看答案與解釋(2, 4, [2, 1, 0, 0, 0], 0, [39, 13, 0, 0, 0], exact_Picard_orbit)

Wave6第十層核對=(2, 4, [2, 1, 0, 0, 0], 0, [39, 13, 0, 0, 0], exact_Picard_orbit)；依完整明示資料獨立重算；Picard orbit、unique fixed point與geometric tail bound使用exact arithmetic；q=1、非self-map、noncomplete或sampled-pairs不足；finite model不取代一般定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r01-contraction-mapping-theorem-0038/)

壓縮映射定理 · qf-mod47-contract-picard-orbit · candidate





## 39. 壓縮映射定理

完整metric、total self-map與forall-pairs q<1 contraction責任。操作=contract-picard-orbit；資料={"metric":[[0,14,42],[14,0,28],[42,28,0]],"mapping":[0,0,1],"q":[1,2],"start":2,"steps":5}。請依 [start, steps, orbit, fixed_point, distances_to_fixed_point, certificate] 欄序回答。

查看答案與解釋(2, 5, [2, 1, 0, 0, 0, 0], 0, [42, 14, 0, 0, 0, 0], exact_Picard_orbit)

Wave6第十層核對=(2, 5, [2, 1, 0, 0, 0, 0], 0, [42, 14, 0, 0, 0, 0], exact_Picard_orbit)；依完整明示資料獨立重算；Picard orbit、unique fixed point與geometric tail bound使用exact arithmetic；q=1、非self-map、noncomplete或sampled-pairs不足；finite model不取代一般定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r01-contraction-mapping-theorem-0039/)

壓縮映射定理 · qf-mod47-contract-picard-orbit · candidate





## 40. 壓縮映射定理

完整metric、total self-map與forall-pairs q<1 contraction責任。操作=contract-picard-orbit；資料={"metric":[[0,15,45],[15,0,30],[45,30,0]],"mapping":[0,0,1],"q":[1,2],"start":2,"steps":6}。請依 [start, steps, orbit, fixed_point, distances_to_fixed_point, certificate] 欄序回答。

查看答案與解釋(2, 6, [2, 1, 0, 0, 0, 0, 0], 0, [45, 15, 0, 0, 0, 0, 0], exact_Picard_orbit)

Wave6第十層核對=(2, 6, [2, 1, 0, 0, 0, 0, 0], 0, [45, 15, 0, 0, 0, 0, 0], exact_Picard_orbit)；依完整明示資料獨立重算；Picard orbit、unique fixed point與geometric tail bound使用exact arithmetic；q=1、非self-map、noncomplete或sampled-pairs不足；finite model不取代一般定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r01-contraction-mapping-theorem-0040/)

壓縮映射定理 · qf-mod47-contract-picard-orbit · candidate





## 41. 壓縮映射定理

完整metric、total self-map與forall-pairs q<1 contraction責任。操作=contract-picard-orbit；資料={"metric":[[0,16,48],[16,0,32],[48,32,0]],"mapping":[0,0,1],"q":[1,2],"start":2,"steps":2}。請依 [start, steps, orbit, fixed_point, distances_to_fixed_point, certificate] 欄序回答。

查看答案與解釋(2, 2, [2, 1, 0], 0, [48, 16, 0], exact_Picard_orbit)

Wave6第十層核對=(2, 2, [2, 1, 0], 0, [48, 16, 0], exact_Picard_orbit)；依完整明示資料獨立重算；Picard orbit、unique fixed point與geometric tail bound使用exact arithmetic；q=1、非self-map、noncomplete或sampled-pairs不足；finite model不取代一般定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r01-contraction-mapping-theorem-0041/)

壓縮映射定理 · qf-mod47-contract-picard-orbit · candidate





## 42. 壓縮映射定理

完整metric、total self-map與forall-pairs q<1 contraction責任。操作=contract-picard-orbit；資料={"metric":[[0,17,51],[17,0,34],[51,34,0]],"mapping":[0,0,1],"q":[1,2],"start":2,"steps":3}。請依 [start, steps, orbit, fixed_point, distances_to_fixed_point, certificate] 欄序回答。

查看答案與解釋(2, 3, [2, 1, 0, 0], 0, [51, 17, 0, 0], exact_Picard_orbit)

Wave6第十層核對=(2, 3, [2, 1, 0, 0], 0, [51, 17, 0, 0], exact_Picard_orbit)；依完整明示資料獨立重算；Picard orbit、unique fixed point與geometric tail bound使用exact arithmetic；q=1、非self-map、noncomplete或sampled-pairs不足；finite model不取代一般定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r01-contraction-mapping-theorem-0042/)

壓縮映射定理 · qf-mod47-contract-picard-orbit · candidate





## 43. 壓縮映射定理

完整metric、total self-map與forall-pairs q<1 contraction責任。操作=contract-picard-orbit；資料={"metric":[[0,18,54],[18,0,36],[54,36,0]],"mapping":[0,0,1],"q":[1,2],"start":2,"steps":4}。請依 [start, steps, orbit, fixed_point, distances_to_fixed_point, certificate] 欄序回答。

查看答案與解釋(2, 4, [2, 1, 0, 0, 0], 0, [54, 18, 0, 0, 0], exact_Picard_orbit)

Wave6第十層核對=(2, 4, [2, 1, 0, 0, 0], 0, [54, 18, 0, 0, 0], exact_Picard_orbit)；依完整明示資料獨立重算；Picard orbit、unique fixed point與geometric tail bound使用exact arithmetic；q=1、非self-map、noncomplete或sampled-pairs不足；finite model不取代一般定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r01-contraction-mapping-theorem-0043/)

壓縮映射定理 · qf-mod47-contract-picard-orbit · candidate





## 44. 壓縮映射定理

完整metric、total self-map與forall-pairs q<1 contraction責任。操作=contract-picard-orbit；資料={"metric":[[0,19,57],[19,0,38],[57,38,0]],"mapping":[0,0,1],"q":[1,2],"start":2,"steps":5}。請依 [start, steps, orbit, fixed_point, distances_to_fixed_point, certificate] 欄序回答。

查看答案與解釋(2, 5, [2, 1, 0, 0, 0, 0], 0, [57, 19, 0, 0, 0, 0], exact_Picard_orbit)

Wave6第十層核對=(2, 5, [2, 1, 0, 0, 0, 0], 0, [57, 19, 0, 0, 0, 0], exact_Picard_orbit)；依完整明示資料獨立重算；Picard orbit、unique fixed point與geometric tail bound使用exact arithmetic；q=1、非self-map、noncomplete或sampled-pairs不足；finite model不取代一般定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r01-contraction-mapping-theorem-0044/)

壓縮映射定理 · qf-mod47-contract-picard-orbit · candidate





## 45. 壓縮映射定理

完整metric、total self-map與forall-pairs q<1 contraction責任。操作=contract-picard-orbit；資料={"metric":[[0,20,60],[20,0,40],[60,40,0]],"mapping":[0,0,1],"q":[1,2],"start":2,"steps":6}。請依 [start, steps, orbit, fixed_point, distances_to_fixed_point, certificate] 欄序回答。

查看答案與解釋(2, 6, [2, 1, 0, 0, 0, 0, 0], 0, [60, 20, 0, 0, 0, 0, 0], exact_Picard_orbit)

Wave6第十層核對=(2, 6, [2, 1, 0, 0, 0, 0, 0], 0, [60, 20, 0, 0, 0, 0, 0], exact_Picard_orbit)；依完整明示資料獨立重算；Picard orbit、unique fixed point與geometric tail bound使用exact arithmetic；q=1、非self-map、noncomplete或sampled-pairs不足；finite model不取代一般定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r01-contraction-mapping-theorem-0045/)

壓縮映射定理 · qf-mod47-contract-picard-orbit · candidate





## 46. 壓縮映射定理

完整metric、total self-map與forall-pairs q<1 contraction責任。操作=contract-picard-orbit；資料={"metric":[[0,21,63],[21,0,42],[63,42,0]],"mapping":[0,0,1],"q":[1,2],"start":2,"steps":2}。請依 [start, steps, orbit, fixed_point, distances_to_fixed_point, certificate] 欄序回答。

查看答案與解釋(2, 2, [2, 1, 0], 0, [63, 21, 0], exact_Picard_orbit)

Wave6第十層核對=(2, 2, [2, 1, 0], 0, [63, 21, 0], exact_Picard_orbit)；依完整明示資料獨立重算；Picard orbit、unique fixed point與geometric tail bound使用exact arithmetic；q=1、非self-map、noncomplete或sampled-pairs不足；finite model不取代一般定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r01-contraction-mapping-theorem-0046/)

壓縮映射定理 · qf-mod47-contract-picard-orbit · candidate





## 47. 壓縮映射定理

完整metric、total self-map與forall-pairs q<1 contraction責任。操作=contract-picard-orbit；資料={"metric":[[0,22,66],[22,0,44],[66,44,0]],"mapping":[0,0,1],"q":[1,2],"start":2,"steps":3}。請依 [start, steps, orbit, fixed_point, distances_to_fixed_point, certificate] 欄序回答。

查看答案與解釋(2, 3, [2, 1, 0, 0], 0, [66, 22, 0, 0], exact_Picard_orbit)

Wave6第十層核對=(2, 3, [2, 1, 0, 0], 0, [66, 22, 0, 0], exact_Picard_orbit)；依完整明示資料獨立重算；Picard orbit、unique fixed point與geometric tail bound使用exact arithmetic；q=1、非self-map、noncomplete或sampled-pairs不足；finite model不取代一般定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r01-contraction-mapping-theorem-0047/)

壓縮映射定理 · qf-mod47-contract-picard-orbit · candidate





## 48. 壓縮映射定理

完整metric、total self-map與forall-pairs q<1 contraction責任。操作=contract-picard-orbit；資料={"metric":[[0,23,69],[23,0,46],[69,46,0]],"mapping":[0,0,1],"q":[1,2],"start":2,"steps":4}。請依 [start, steps, orbit, fixed_point, distances_to_fixed_point, certificate] 欄序回答。

查看答案與解釋(2, 4, [2, 1, 0, 0, 0], 0, [69, 23, 0, 0, 0], exact_Picard_orbit)

Wave6第十層核對=(2, 4, [2, 1, 0, 0, 0], 0, [69, 23, 0, 0, 0], exact_Picard_orbit)；依完整明示資料獨立重算；Picard orbit、unique fixed point與geometric tail bound使用exact arithmetic；q=1、非self-map、noncomplete或sampled-pairs不足；finite model不取代一般定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r01-contraction-mapping-theorem-0048/)

壓縮映射定理 · qf-mod47-contract-picard-orbit · candidate





## 49. 壓縮映射定理

完整metric、total self-map與forall-pairs q<1 contraction責任。操作=contract-picard-orbit；資料={"metric":[[0,24,72],[24,0,48],[72,48,0]],"mapping":[0,0,1],"q":[1,2],"start":2,"steps":5}。請依 [start, steps, orbit, fixed_point, distances_to_fixed_point, certificate] 欄序回答。

查看答案與解釋(2, 5, [2, 1, 0, 0, 0, 0], 0, [72, 24, 0, 0, 0, 0], exact_Picard_orbit)

Wave6第十層核對=(2, 5, [2, 1, 0, 0, 0, 0], 0, [72, 24, 0, 0, 0, 0], exact_Picard_orbit)；依完整明示資料獨立重算；Picard orbit、unique fixed point與geometric tail bound使用exact arithmetic；q=1、非self-map、noncomplete或sampled-pairs不足；finite model不取代一般定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r01-contraction-mapping-theorem-0049/)

壓縮映射定理 · qf-mod47-contract-picard-orbit · candidate





## 50. 壓縮映射定理

完整metric、total self-map與forall-pairs q<1 contraction責任。操作=contract-picard-orbit；資料={"metric":[[0,25,75],[25,0,50],[75,50,0]],"mapping":[0,0,1],"q":[1,2],"start":2,"steps":6}。請依 [start, steps, orbit, fixed_point, distances_to_fixed_point, certificate] 欄序回答。

查看答案與解釋(2, 6, [2, 1, 0, 0, 0, 0, 0], 0, [75, 25, 0, 0, 0, 0, 0], exact_Picard_orbit)

Wave6第十層核對=(2, 6, [2, 1, 0, 0, 0, 0, 0], 0, [75, 25, 0, 0, 0, 0, 0], exact_Picard_orbit)；依完整明示資料獨立重算；Picard orbit、unique fixed point與geometric tail bound使用exact arithmetic；q=1、非self-map、noncomplete或sampled-pairs不足；finite model不取代一般定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r01-contraction-mapping-theorem-0050/)

壓縮映射定理 · qf-mod47-contract-picard-orbit · candidate





## 51. 壓縮映射定理

完整metric、total self-map與forall-pairs q<1 contraction責任。操作=contract-fixed-point-bound；資料={"metric":[[0,1,3],[1,0,2],[3,2,0]],"mapping":[0,0,1],"q":[1,2],"start":2,"steps":2}。請依 [orbit, fixed_point, actual_error, geometric_bound, bound_holds, certificate] 欄序回答。

查看答案與解釋([2, 1, 0], 0, 0, 1, 是, d_xn_fixed_le_qn_over_one_minus_q_times_d_x1_x0)

Wave6第十層核對=([2, 1, 0], 0, 0, 1, 是, d_xn_fixed_le_qn_over_one_minus_q_times_d_x1_x0)；依完整明示資料獨立重算；Picard orbit、unique fixed point與geometric tail bound使用exact arithmetic；q=1、非self-map、noncomplete或sampled-pairs不足；finite model不取代一般定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r01-contraction-mapping-theorem-0051/)

壓縮映射定理 · qf-mod47-contract-fixed-point-bound · candidate





## 52. 壓縮映射定理

完整metric、total self-map與forall-pairs q<1 contraction責任。操作=contract-fixed-point-bound；資料={"metric":[[0,2,6],[2,0,4],[6,4,0]],"mapping":[0,0,1],"q":[1,2],"start":2,"steps":3}。請依 [orbit, fixed_point, actual_error, geometric_bound, bound_holds, certificate] 欄序回答。

查看答案與解釋([2, 1, 0, 0], 0, 0, 1, 是, d_xn_fixed_le_qn_over_one_minus_q_times_d_x1_x0)

Wave6第十層核對=([2, 1, 0, 0], 0, 0, 1, 是, d_xn_fixed_le_qn_over_one_minus_q_times_d_x1_x0)；依完整明示資料獨立重算；Picard orbit、unique fixed point與geometric tail bound使用exact arithmetic；q=1、非self-map、noncomplete或sampled-pairs不足；finite model不取代一般定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r01-contraction-mapping-theorem-0052/)

壓縮映射定理 · qf-mod47-contract-fixed-point-bound · candidate





## 53. 壓縮映射定理

完整metric、total self-map與forall-pairs q<1 contraction責任。操作=contract-fixed-point-bound；資料={"metric":[[0,3,9],[3,0,6],[9,6,0]],"mapping":[0,0,1],"q":[1,2],"start":2,"steps":4}。請依 [orbit, fixed_point, actual_error, geometric_bound, bound_holds, certificate] 欄序回答。

查看答案與解釋([2, 1, 0, 0, 0], 0, 0, 3/4, 是, d_xn_fixed_le_qn_over_one_minus_q_times_d_x1_x0)

Wave6第十層核對=([2, 1, 0, 0, 0], 0, 0, 3/4, 是, d_xn_fixed_le_qn_over_one_minus_q_times_d_x1_x0)；依完整明示資料獨立重算；Picard orbit、unique fixed point與geometric tail bound使用exact arithmetic；q=1、非self-map、noncomplete或sampled-pairs不足；finite model不取代一般定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r01-contraction-mapping-theorem-0053/)

壓縮映射定理 · qf-mod47-contract-fixed-point-bound · candidate





## 54. 壓縮映射定理

完整metric、total self-map與forall-pairs q<1 contraction責任。操作=contract-fixed-point-bound；資料={"metric":[[0,4,12],[4,0,8],[12,8,0]],"mapping":[0,0,1],"q":[1,2],"start":2,"steps":5}。請依 [orbit, fixed_point, actual_error, geometric_bound, bound_holds, certificate] 欄序回答。

查看答案與解釋([2, 1, 0, 0, 0, 0], 0, 0, 1/2, 是, d_xn_fixed_le_qn_over_one_minus_q_times_d_x1_x0)

Wave6第十層核對=([2, 1, 0, 0, 0, 0], 0, 0, 1/2, 是, d_xn_fixed_le_qn_over_one_minus_q_times_d_x1_x0)；依完整明示資料獨立重算；Picard orbit、unique fixed point與geometric tail bound使用exact arithmetic；q=1、非self-map、noncomplete或sampled-pairs不足；finite model不取代一般定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r01-contraction-mapping-theorem-0054/)

壓縮映射定理 · qf-mod47-contract-fixed-point-bound · candidate





## 55. 壓縮映射定理

完整metric、total self-map與forall-pairs q<1 contraction責任。操作=contract-fixed-point-bound；資料={"metric":[[0,5,15],[5,0,10],[15,10,0]],"mapping":[0,0,1],"q":[1,2],"start":2,"steps":6}。請依 [orbit, fixed_point, actual_error, geometric_bound, bound_holds, certificate] 欄序回答。

查看答案與解釋([2, 1, 0, 0, 0, 0, 0], 0, 0, 5/16, 是, d_xn_fixed_le_qn_over_one_minus_q_times_d_x1_x0)

Wave6第十層核對=([2, 1, 0, 0, 0, 0, 0], 0, 0, 5/16, 是, d_xn_fixed_le_qn_over_one_minus_q_times_d_x1_x0)；依完整明示資料獨立重算；Picard orbit、unique fixed point與geometric tail bound使用exact arithmetic；q=1、非self-map、noncomplete或sampled-pairs不足；finite model不取代一般定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r01-contraction-mapping-theorem-0055/)

壓縮映射定理 · qf-mod47-contract-fixed-point-bound · candidate





## 56. 壓縮映射定理

完整metric、total self-map與forall-pairs q<1 contraction責任。操作=contract-fixed-point-bound；資料={"metric":[[0,6,18],[6,0,12],[18,12,0]],"mapping":[0,0,1],"q":[1,2],"start":2,"steps":2}。請依 [orbit, fixed_point, actual_error, geometric_bound, bound_holds, certificate] 欄序回答。

查看答案與解釋([2, 1, 0], 0, 0, 6, 是, d_xn_fixed_le_qn_over_one_minus_q_times_d_x1_x0)

Wave6第十層核對=([2, 1, 0], 0, 0, 6, 是, d_xn_fixed_le_qn_over_one_minus_q_times_d_x1_x0)；依完整明示資料獨立重算；Picard orbit、unique fixed point與geometric tail bound使用exact arithmetic；q=1、非self-map、noncomplete或sampled-pairs不足；finite model不取代一般定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r01-contraction-mapping-theorem-0056/)

壓縮映射定理 · qf-mod47-contract-fixed-point-bound · candidate





## 57. 壓縮映射定理

完整metric、total self-map與forall-pairs q<1 contraction責任。操作=contract-fixed-point-bound；資料={"metric":[[0,7,21],[7,0,14],[21,14,0]],"mapping":[0,0,1],"q":[1,2],"start":2,"steps":3}。請依 [orbit, fixed_point, actual_error, geometric_bound, bound_holds, certificate] 欄序回答。

查看答案與解釋([2, 1, 0, 0], 0, 0, 7/2, 是, d_xn_fixed_le_qn_over_one_minus_q_times_d_x1_x0)

Wave6第十層核對=([2, 1, 0, 0], 0, 0, 7/2, 是, d_xn_fixed_le_qn_over_one_minus_q_times_d_x1_x0)；依完整明示資料獨立重算；Picard orbit、unique fixed point與geometric tail bound使用exact arithmetic；q=1、非self-map、noncomplete或sampled-pairs不足；finite model不取代一般定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r01-contraction-mapping-theorem-0057/)

壓縮映射定理 · qf-mod47-contract-fixed-point-bound · candidate





## 58. 壓縮映射定理

完整metric、total self-map與forall-pairs q<1 contraction責任。操作=contract-fixed-point-bound；資料={"metric":[[0,8,24],[8,0,16],[24,16,0]],"mapping":[0,0,1],"q":[1,2],"start":2,"steps":4}。請依 [orbit, fixed_point, actual_error, geometric_bound, bound_holds, certificate] 欄序回答。

查看答案與解釋([2, 1, 0, 0, 0], 0, 0, 2, 是, d_xn_fixed_le_qn_over_one_minus_q_times_d_x1_x0)

Wave6第十層核對=([2, 1, 0, 0, 0], 0, 0, 2, 是, d_xn_fixed_le_qn_over_one_minus_q_times_d_x1_x0)；依完整明示資料獨立重算；Picard orbit、unique fixed point與geometric tail bound使用exact arithmetic；q=1、非self-map、noncomplete或sampled-pairs不足；finite model不取代一般定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r01-contraction-mapping-theorem-0058/)

壓縮映射定理 · qf-mod47-contract-fixed-point-bound · candidate





## 59. 壓縮映射定理

完整metric、total self-map與forall-pairs q<1 contraction責任。操作=contract-fixed-point-bound；資料={"metric":[[0,9,27],[9,0,18],[27,18,0]],"mapping":[0,0,1],"q":[1,2],"start":2,"steps":5}。請依 [orbit, fixed_point, actual_error, geometric_bound, bound_holds, certificate] 欄序回答。

查看答案與解釋([2, 1, 0, 0, 0, 0], 0, 0, 9/8, 是, d_xn_fixed_le_qn_over_one_minus_q_times_d_x1_x0)

Wave6第十層核對=([2, 1, 0, 0, 0, 0], 0, 0, 9/8, 是, d_xn_fixed_le_qn_over_one_minus_q_times_d_x1_x0)；依完整明示資料獨立重算；Picard orbit、unique fixed point與geometric tail bound使用exact arithmetic；q=1、非self-map、noncomplete或sampled-pairs不足；finite model不取代一般定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r01-contraction-mapping-theorem-0059/)

壓縮映射定理 · qf-mod47-contract-fixed-point-bound · candidate





## 60. 壓縮映射定理

完整metric、total self-map與forall-pairs q<1 contraction責任。操作=contract-fixed-point-bound；資料={"metric":[[0,10,30],[10,0,20],[30,20,0]],"mapping":[0,0,1],"q":[1,2],"start":2,"steps":6}。請依 [orbit, fixed_point, actual_error, geometric_bound, bound_holds, certificate] 欄序回答。

查看答案與解釋([2, 1, 0, 0, 0, 0, 0], 0, 0, 5/8, 是, d_xn_fixed_le_qn_over_one_minus_q_times_d_x1_x0)

Wave6第十層核對=([2, 1, 0, 0, 0, 0, 0], 0, 0, 5/8, 是, d_xn_fixed_le_qn_over_one_minus_q_times_d_x1_x0)；依完整明示資料獨立重算；Picard orbit、unique fixed point與geometric tail bound使用exact arithmetic；q=1、非self-map、noncomplete或sampled-pairs不足；finite model不取代一般定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r01-contraction-mapping-theorem-0060/)

壓縮映射定理 · qf-mod47-contract-fixed-point-bound · candidate





## 61. 壓縮映射定理

完整metric、total self-map與forall-pairs q<1 contraction責任。操作=contract-fixed-point-bound；資料={"metric":[[0,11,33],[11,0,22],[33,22,0]],"mapping":[0,0,1],"q":[1,2],"start":2,"steps":2}。請依 [orbit, fixed_point, actual_error, geometric_bound, bound_holds, certificate] 欄序回答。

查看答案與解釋([2, 1, 0], 0, 0, 11, 是, d_xn_fixed_le_qn_over_one_minus_q_times_d_x1_x0)

Wave6第十層核對=([2, 1, 0], 0, 0, 11, 是, d_xn_fixed_le_qn_over_one_minus_q_times_d_x1_x0)；依完整明示資料獨立重算；Picard orbit、unique fixed point與geometric tail bound使用exact arithmetic；q=1、非self-map、noncomplete或sampled-pairs不足；finite model不取代一般定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r01-contraction-mapping-theorem-0061/)

壓縮映射定理 · qf-mod47-contract-fixed-point-bound · candidate





## 62. 壓縮映射定理

完整metric、total self-map與forall-pairs q<1 contraction責任。操作=contract-fixed-point-bound；資料={"metric":[[0,12,36],[12,0,24],[36,24,0]],"mapping":[0,0,1],"q":[1,2],"start":2,"steps":3}。請依 [orbit, fixed_point, actual_error, geometric_bound, bound_holds, certificate] 欄序回答。

查看答案與解釋([2, 1, 0, 0], 0, 0, 6, 是, d_xn_fixed_le_qn_over_one_minus_q_times_d_x1_x0)

Wave6第十層核對=([2, 1, 0, 0], 0, 0, 6, 是, d_xn_fixed_le_qn_over_one_minus_q_times_d_x1_x0)；依完整明示資料獨立重算；Picard orbit、unique fixed point與geometric tail bound使用exact arithmetic；q=1、非self-map、noncomplete或sampled-pairs不足；finite model不取代一般定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r01-contraction-mapping-theorem-0062/)

壓縮映射定理 · qf-mod47-contract-fixed-point-bound · candidate





## 63. 壓縮映射定理

完整metric、total self-map與forall-pairs q<1 contraction責任。操作=contract-fixed-point-bound；資料={"metric":[[0,13,39],[13,0,26],[39,26,0]],"mapping":[0,0,1],"q":[1,2],"start":2,"steps":4}。請依 [orbit, fixed_point, actual_error, geometric_bound, bound_holds, certificate] 欄序回答。

查看答案與解釋([2, 1, 0, 0, 0], 0, 0, 13/4, 是, d_xn_fixed_le_qn_over_one_minus_q_times_d_x1_x0)

Wave6第十層核對=([2, 1, 0, 0, 0], 0, 0, 13/4, 是, d_xn_fixed_le_qn_over_one_minus_q_times_d_x1_x0)；依完整明示資料獨立重算；Picard orbit、unique fixed point與geometric tail bound使用exact arithmetic；q=1、非self-map、noncomplete或sampled-pairs不足；finite model不取代一般定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r01-contraction-mapping-theorem-0063/)

壓縮映射定理 · qf-mod47-contract-fixed-point-bound · candidate





## 64. 壓縮映射定理

完整metric、total self-map與forall-pairs q<1 contraction責任。操作=contract-fixed-point-bound；資料={"metric":[[0,14,42],[14,0,28],[42,28,0]],"mapping":[0,0,1],"q":[1,2],"start":2,"steps":5}。請依 [orbit, fixed_point, actual_error, geometric_bound, bound_holds, certificate] 欄序回答。

查看答案與解釋([2, 1, 0, 0, 0, 0], 0, 0, 7/4, 是, d_xn_fixed_le_qn_over_one_minus_q_times_d_x1_x0)

Wave6第十層核對=([2, 1, 0, 0, 0, 0], 0, 0, 7/4, 是, d_xn_fixed_le_qn_over_one_minus_q_times_d_x1_x0)；依完整明示資料獨立重算；Picard orbit、unique fixed point與geometric tail bound使用exact arithmetic；q=1、非self-map、noncomplete或sampled-pairs不足；finite model不取代一般定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r01-contraction-mapping-theorem-0064/)

壓縮映射定理 · qf-mod47-contract-fixed-point-bound · candidate





## 65. 壓縮映射定理

完整metric、total self-map與forall-pairs q<1 contraction責任。操作=contract-fixed-point-bound；資料={"metric":[[0,15,45],[15,0,30],[45,30,0]],"mapping":[0,0,1],"q":[1,2],"start":2,"steps":6}。請依 [orbit, fixed_point, actual_error, geometric_bound, bound_holds, certificate] 欄序回答。

查看答案與解釋([2, 1, 0, 0, 0, 0, 0], 0, 0, 15/16, 是, d_xn_fixed_le_qn_over_one_minus_q_times_d_x1_x0)

Wave6第十層核對=([2, 1, 0, 0, 0, 0, 0], 0, 0, 15/16, 是, d_xn_fixed_le_qn_over_one_minus_q_times_d_x1_x0)；依完整明示資料獨立重算；Picard orbit、unique fixed point與geometric tail bound使用exact arithmetic；q=1、非self-map、noncomplete或sampled-pairs不足；finite model不取代一般定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r01-contraction-mapping-theorem-0065/)

壓縮映射定理 · qf-mod47-contract-fixed-point-bound · candidate





## 66. 壓縮映射定理

完整metric、total self-map與forall-pairs q<1 contraction責任。操作=contract-fixed-point-bound；資料={"metric":[[0,16,48],[16,0,32],[48,32,0]],"mapping":[0,0,1],"q":[1,2],"start":2,"steps":2}。請依 [orbit, fixed_point, actual_error, geometric_bound, bound_holds, certificate] 欄序回答。

查看答案與解釋([2, 1, 0], 0, 0, 16, 是, d_xn_fixed_le_qn_over_one_minus_q_times_d_x1_x0)

Wave6第十層核對=([2, 1, 0], 0, 0, 16, 是, d_xn_fixed_le_qn_over_one_minus_q_times_d_x1_x0)；依完整明示資料獨立重算；Picard orbit、unique fixed point與geometric tail bound使用exact arithmetic；q=1、非self-map、noncomplete或sampled-pairs不足；finite model不取代一般定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r01-contraction-mapping-theorem-0066/)

壓縮映射定理 · qf-mod47-contract-fixed-point-bound · candidate





## 67. 壓縮映射定理

完整metric、total self-map與forall-pairs q<1 contraction責任。操作=contract-fixed-point-bound；資料={"metric":[[0,17,51],[17,0,34],[51,34,0]],"mapping":[0,0,1],"q":[1,2],"start":2,"steps":3}。請依 [orbit, fixed_point, actual_error, geometric_bound, bound_holds, certificate] 欄序回答。

查看答案與解釋([2, 1, 0, 0], 0, 0, 17/2, 是, d_xn_fixed_le_qn_over_one_minus_q_times_d_x1_x0)

Wave6第十層核對=([2, 1, 0, 0], 0, 0, 17/2, 是, d_xn_fixed_le_qn_over_one_minus_q_times_d_x1_x0)；依完整明示資料獨立重算；Picard orbit、unique fixed point與geometric tail bound使用exact arithmetic；q=1、非self-map、noncomplete或sampled-pairs不足；finite model不取代一般定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r01-contraction-mapping-theorem-0067/)

壓縮映射定理 · qf-mod47-contract-fixed-point-bound · candidate





## 68. 壓縮映射定理

完整metric、total self-map與forall-pairs q<1 contraction責任。操作=contract-fixed-point-bound；資料={"metric":[[0,18,54],[18,0,36],[54,36,0]],"mapping":[0,0,1],"q":[1,2],"start":2,"steps":4}。請依 [orbit, fixed_point, actual_error, geometric_bound, bound_holds, certificate] 欄序回答。

查看答案與解釋([2, 1, 0, 0, 0], 0, 0, 9/2, 是, d_xn_fixed_le_qn_over_one_minus_q_times_d_x1_x0)

Wave6第十層核對=([2, 1, 0, 0, 0], 0, 0, 9/2, 是, d_xn_fixed_le_qn_over_one_minus_q_times_d_x1_x0)；依完整明示資料獨立重算；Picard orbit、unique fixed point與geometric tail bound使用exact arithmetic；q=1、非self-map、noncomplete或sampled-pairs不足；finite model不取代一般定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r01-contraction-mapping-theorem-0068/)

壓縮映射定理 · qf-mod47-contract-fixed-point-bound · candidate





## 69. 壓縮映射定理

完整metric、total self-map與forall-pairs q<1 contraction責任。操作=contract-fixed-point-bound；資料={"metric":[[0,19,57],[19,0,38],[57,38,0]],"mapping":[0,0,1],"q":[1,2],"start":2,"steps":5}。請依 [orbit, fixed_point, actual_error, geometric_bound, bound_holds, certificate] 欄序回答。

查看答案與解釋([2, 1, 0, 0, 0, 0], 0, 0, 19/8, 是, d_xn_fixed_le_qn_over_one_minus_q_times_d_x1_x0)

Wave6第十層核對=([2, 1, 0, 0, 0, 0], 0, 0, 19/8, 是, d_xn_fixed_le_qn_over_one_minus_q_times_d_x1_x0)；依完整明示資料獨立重算；Picard orbit、unique fixed point與geometric tail bound使用exact arithmetic；q=1、非self-map、noncomplete或sampled-pairs不足；finite model不取代一般定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r01-contraction-mapping-theorem-0069/)

壓縮映射定理 · qf-mod47-contract-fixed-point-bound · candidate





## 70. 壓縮映射定理

完整metric、total self-map與forall-pairs q<1 contraction責任。操作=contract-fixed-point-bound；資料={"metric":[[0,20,60],[20,0,40],[60,40,0]],"mapping":[0,0,1],"q":[1,2],"start":2,"steps":6}。請依 [orbit, fixed_point, actual_error, geometric_bound, bound_holds, certificate] 欄序回答。

查看答案與解釋([2, 1, 0, 0, 0, 0, 0], 0, 0, 5/4, 是, d_xn_fixed_le_qn_over_one_minus_q_times_d_x1_x0)

Wave6第十層核對=([2, 1, 0, 0, 0, 0, 0], 0, 0, 5/4, 是, d_xn_fixed_le_qn_over_one_minus_q_times_d_x1_x0)；依完整明示資料獨立重算；Picard orbit、unique fixed point與geometric tail bound使用exact arithmetic；q=1、非self-map、noncomplete或sampled-pairs不足；finite model不取代一般定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r01-contraction-mapping-theorem-0070/)

壓縮映射定理 · qf-mod47-contract-fixed-point-bound · candidate





## 71. 壓縮映射定理

完整metric、total self-map與forall-pairs q<1 contraction責任。操作=contract-fixed-point-bound；資料={"metric":[[0,21,63],[21,0,42],[63,42,0]],"mapping":[0,0,1],"q":[1,2],"start":2,"steps":2}。請依 [orbit, fixed_point, actual_error, geometric_bound, bound_holds, certificate] 欄序回答。

查看答案與解釋([2, 1, 0], 0, 0, 21, 是, d_xn_fixed_le_qn_over_one_minus_q_times_d_x1_x0)

Wave6第十層核對=([2, 1, 0], 0, 0, 21, 是, d_xn_fixed_le_qn_over_one_minus_q_times_d_x1_x0)；依完整明示資料獨立重算；Picard orbit、unique fixed point與geometric tail bound使用exact arithmetic；q=1、非self-map、noncomplete或sampled-pairs不足；finite model不取代一般定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r01-contraction-mapping-theorem-0071/)

壓縮映射定理 · qf-mod47-contract-fixed-point-bound · candidate





## 72. 壓縮映射定理

完整metric、total self-map與forall-pairs q<1 contraction責任。操作=contract-fixed-point-bound；資料={"metric":[[0,22,66],[22,0,44],[66,44,0]],"mapping":[0,0,1],"q":[1,2],"start":2,"steps":3}。請依 [orbit, fixed_point, actual_error, geometric_bound, bound_holds, certificate] 欄序回答。

查看答案與解釋([2, 1, 0, 0], 0, 0, 11, 是, d_xn_fixed_le_qn_over_one_minus_q_times_d_x1_x0)

Wave6第十層核對=([2, 1, 0, 0], 0, 0, 11, 是, d_xn_fixed_le_qn_over_one_minus_q_times_d_x1_x0)；依完整明示資料獨立重算；Picard orbit、unique fixed point與geometric tail bound使用exact arithmetic；q=1、非self-map、noncomplete或sampled-pairs不足；finite model不取代一般定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r01-contraction-mapping-theorem-0072/)

壓縮映射定理 · qf-mod47-contract-fixed-point-bound · candidate





## 73. 壓縮映射定理

完整metric、total self-map與forall-pairs q<1 contraction責任。操作=contract-fixed-point-bound；資料={"metric":[[0,23,69],[23,0,46],[69,46,0]],"mapping":[0,0,1],"q":[1,2],"start":2,"steps":4}。請依 [orbit, fixed_point, actual_error, geometric_bound, bound_holds, certificate] 欄序回答。

查看答案與解釋([2, 1, 0, 0, 0], 0, 0, 23/4, 是, d_xn_fixed_le_qn_over_one_minus_q_times_d_x1_x0)

Wave6第十層核對=([2, 1, 0, 0, 0], 0, 0, 23/4, 是, d_xn_fixed_le_qn_over_one_minus_q_times_d_x1_x0)；依完整明示資料獨立重算；Picard orbit、unique fixed point與geometric tail bound使用exact arithmetic；q=1、非self-map、noncomplete或sampled-pairs不足；finite model不取代一般定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r01-contraction-mapping-theorem-0073/)

壓縮映射定理 · qf-mod47-contract-fixed-point-bound · candidate





## 74. 壓縮映射定理

完整metric、total self-map與forall-pairs q<1 contraction責任。操作=contract-fixed-point-bound；資料={"metric":[[0,24,72],[24,0,48],[72,48,0]],"mapping":[0,0,1],"q":[1,2],"start":2,"steps":5}。請依 [orbit, fixed_point, actual_error, geometric_bound, bound_holds, certificate] 欄序回答。

查看答案與解釋([2, 1, 0, 0, 0, 0], 0, 0, 3, 是, d_xn_fixed_le_qn_over_one_minus_q_times_d_x1_x0)

Wave6第十層核對=([2, 1, 0, 0, 0, 0], 0, 0, 3, 是, d_xn_fixed_le_qn_over_one_minus_q_times_d_x1_x0)；依完整明示資料獨立重算；Picard orbit、unique fixed point與geometric tail bound使用exact arithmetic；q=1、非self-map、noncomplete或sampled-pairs不足；finite model不取代一般定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r01-contraction-mapping-theorem-0074/)

壓縮映射定理 · qf-mod47-contract-fixed-point-bound · candidate





## 75. 壓縮映射定理

完整metric、total self-map與forall-pairs q<1 contraction責任。操作=contract-fixed-point-bound；資料={"metric":[[0,25,75],[25,0,50],[75,50,0]],"mapping":[0,0,1],"q":[1,2],"start":2,"steps":6}。請依 [orbit, fixed_point, actual_error, geometric_bound, bound_holds, certificate] 欄序回答。

查看答案與解釋([2, 1, 0, 0, 0, 0, 0], 0, 0, 25/16, 是, d_xn_fixed_le_qn_over_one_minus_q_times_d_x1_x0)

Wave6第十層核對=([2, 1, 0, 0, 0, 0, 0], 0, 0, 25/16, 是, d_xn_fixed_le_qn_over_one_minus_q_times_d_x1_x0)；依完整明示資料獨立重算；Picard orbit、unique fixed point與geometric tail bound使用exact arithmetic；q=1、非self-map、noncomplete或sampled-pairs不足；finite model不取代一般定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r01-contraction-mapping-theorem-0075/)

壓縮映射定理 · qf-mod47-contract-fixed-point-bound · candidate





## 76. 壓縮映射定理

完整metric、total self-map與forall-pairs q<1 contraction責任。操作=contract-boundary；資料={"mode":"q_equal_one","scale":1}。請依 [mode, scale, metric_description, q, fixed_point_counterexample, theorem_application_claim] 欄序回答。

q=1、非self-map、非complete與sampled-pairs的6/4/6/6欄角色不同。sampled_pairs只保留來源的範圍敘述，沒有供應可重算的完整反例metric/map。

查看答案與解釋(q_equal_one, 1, two_point_metric, 1, identity_map_has_two_fixed_points, 否)

Wave6第十層核對=(q_equal_one, 1, two_point_metric, 1, identity_map_has_two_fixed_points, 否)；依完整明示資料獨立重算；Picard orbit、unique fixed point與geometric tail bound使用exact arithmetic；q=1、非self-map、noncomplete或sampled-pairs不足；finite model不取代一般定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r01-contraction-mapping-theorem-0076/)

壓縮映射定理 · qf-mod47-contract-boundary · candidate





## 77. 壓縮映射定理

完整metric、total self-map與forall-pairs q<1 contraction責任。操作=contract-boundary；資料={"mode":"non_self_map","scale":2}。請依 [mode, scale, mapping_description, theorem_application_claim] 欄序回答。

q=1、非self-map、非complete與sampled-pairs的6/4/6/6欄角色不同。sampled_pairs只保留來源的範圍敘述，沒有供應可重算的完整反例metric/map。

查看答案與解釋(non_self_map, 2, T_maps_one_point_outside_X, 否)

Wave6第十層核對=(non_self_map, 2, T_maps_one_point_outside_X, 否)；依完整明示資料獨立重算；Picard orbit、unique fixed point與geometric tail bound使用exact arithmetic；q=1、非self-map、noncomplete或sampled-pairs不足；finite model不取代一般定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r01-contraction-mapping-theorem-0077/)

壓縮映射定理 · qf-mod47-contract-boundary · candidate





## 78. 壓縮映射定理

完整metric、total self-map與forall-pairs q<1 contraction責任。操作=contract-boundary；資料={"mode":"noncomplete_space","scale":3}。請依 [mode, space_description, mapping_description, outside_fixed_point, q_as_fraction, theorem_application_claim] 欄序回答。

q=1、非self-map、非complete與sampled-pairs的6/4/6/6欄角色不同。sampled_pairs只保留來源的範圍敘述，沒有供應可重算的完整反例metric/map。

查看答案與解釋(noncomplete_space, X=(0,3), T(x)=(x+3)/2, fixed_point=3_outside_X, [1, 2], 否)

Wave6第十層核對=(noncomplete_space, X=(0,3), T(x)=(x+3)/2, fixed_point=3_outside_X, [1, 2], 否)；依完整明示資料獨立重算；Picard orbit、unique fixed point與geometric tail bound使用exact arithmetic；q=1、非self-map、noncomplete或sampled-pairs不足；finite model不取代一般定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r01-contraction-mapping-theorem-0078/)

壓縮映射定理 · qf-mod47-contract-boundary · candidate





## 79. 壓縮映射定理

完整metric、total self-map與forall-pairs q<1 contraction責任。操作=contract-boundary；資料={"mode":"sampled_pairs","scale":4}。請依 [mode, scale, sampled_pair_result, unchecked_pair_statement, global_contraction_claim, boundary] 欄序回答。

q=1、非self-map、非complete與sampled-pairs的6/4/6/6欄角色不同。sampled_pairs只保留來源的範圍敘述，沒有供應可重算的完整反例metric/map。

查看答案與解釋(sampled_pairs, 4, checked_pairs_pass, one_unchecked_pair_violates_global_bound, 否, sampled_pairs_do_not_prove_global_contraction)

Wave6第十層核對=(sampled_pairs, 4, checked_pairs_pass, one_unchecked_pair_violates_global_bound, 否, sampled_pairs_do_not_prove_global_contraction)；依完整明示資料獨立重算；Picard orbit、unique fixed point與geometric tail bound使用exact arithmetic；q=1、非self-map、noncomplete或sampled-pairs不足；finite model不取代一般定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r01-contraction-mapping-theorem-0079/)

壓縮映射定理 · qf-mod47-contract-boundary · candidate





## 80. 壓縮映射定理

完整metric、total self-map與forall-pairs q<1 contraction責任。操作=contract-boundary；資料={"mode":"q_equal_one","scale":5}。請依 [mode, scale, metric_description, q, fixed_point_counterexample, theorem_application_claim] 欄序回答。

q=1、非self-map、非complete與sampled-pairs的6/4/6/6欄角色不同。sampled_pairs只保留來源的範圍敘述，沒有供應可重算的完整反例metric/map。

查看答案與解釋(q_equal_one, 5, two_point_metric, 1, identity_map_has_two_fixed_points, 否)

Wave6第十層核對=(q_equal_one, 5, two_point_metric, 1, identity_map_has_two_fixed_points, 否)；依完整明示資料獨立重算；Picard orbit、unique fixed point與geometric tail bound使用exact arithmetic；q=1、非self-map、noncomplete或sampled-pairs不足；finite model不取代一般定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r01-contraction-mapping-theorem-0080/)

壓縮映射定理 · qf-mod47-contract-boundary · candidate





## 81. 壓縮映射定理

完整metric、total self-map與forall-pairs q<1 contraction責任。操作=contract-boundary；資料={"mode":"non_self_map","scale":6}。請依 [mode, scale, mapping_description, theorem_application_claim] 欄序回答。

q=1、非self-map、非complete與sampled-pairs的6/4/6/6欄角色不同。sampled_pairs只保留來源的範圍敘述，沒有供應可重算的完整反例metric/map。

查看答案與解釋(non_self_map, 6, T_maps_one_point_outside_X, 否)

Wave6第十層核對=(non_self_map, 6, T_maps_one_point_outside_X, 否)；依完整明示資料獨立重算；Picard orbit、unique fixed point與geometric tail bound使用exact arithmetic；q=1、非self-map、noncomplete或sampled-pairs不足；finite model不取代一般定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r01-contraction-mapping-theorem-0081/)

壓縮映射定理 · qf-mod47-contract-boundary · candidate





## 82. 壓縮映射定理

完整metric、total self-map與forall-pairs q<1 contraction責任。操作=contract-boundary；資料={"mode":"noncomplete_space","scale":7}。請依 [mode, space_description, mapping_description, outside_fixed_point, q_as_fraction, theorem_application_claim] 欄序回答。

q=1、非self-map、非complete與sampled-pairs的6/4/6/6欄角色不同。sampled_pairs只保留來源的範圍敘述，沒有供應可重算的完整反例metric/map。

查看答案與解釋(noncomplete_space, X=(0,7), T(x)=(x+7)/2, fixed_point=7_outside_X, [1, 2], 否)

Wave6第十層核對=(noncomplete_space, X=(0,7), T(x)=(x+7)/2, fixed_point=7_outside_X, [1, 2], 否)；依完整明示資料獨立重算；Picard orbit、unique fixed point與geometric tail bound使用exact arithmetic；q=1、非self-map、noncomplete或sampled-pairs不足；finite model不取代一般定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r01-contraction-mapping-theorem-0082/)

壓縮映射定理 · qf-mod47-contract-boundary · candidate





## 83. 壓縮映射定理

完整metric、total self-map與forall-pairs q<1 contraction責任。操作=contract-boundary；資料={"mode":"sampled_pairs","scale":8}。請依 [mode, scale, sampled_pair_result, unchecked_pair_statement, global_contraction_claim, boundary] 欄序回答。

q=1、非self-map、非complete與sampled-pairs的6/4/6/6欄角色不同。sampled_pairs只保留來源的範圍敘述，沒有供應可重算的完整反例metric/map。

查看答案與解釋(sampled_pairs, 8, checked_pairs_pass, one_unchecked_pair_violates_global_bound, 否, sampled_pairs_do_not_prove_global_contraction)

Wave6第十層核對=(sampled_pairs, 8, checked_pairs_pass, one_unchecked_pair_violates_global_bound, 否, sampled_pairs_do_not_prove_global_contraction)；依完整明示資料獨立重算；Picard orbit、unique fixed point與geometric tail bound使用exact arithmetic；q=1、非self-map、noncomplete或sampled-pairs不足；finite model不取代一般定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r01-contraction-mapping-theorem-0083/)

壓縮映射定理 · qf-mod47-contract-boundary · candidate





## 84. 壓縮映射定理

完整metric、total self-map與forall-pairs q<1 contraction責任。操作=contract-boundary；資料={"mode":"q_equal_one","scale":9}。請依 [mode, scale, metric_description, q, fixed_point_counterexample, theorem_application_claim] 欄序回答。

q=1、非self-map、非complete與sampled-pairs的6/4/6/6欄角色不同。sampled_pairs只保留來源的範圍敘述，沒有供應可重算的完整反例metric/map。

查看答案與解釋(q_equal_one, 9, two_point_metric, 1, identity_map_has_two_fixed_points, 否)

Wave6第十層核對=(q_equal_one, 9, two_point_metric, 1, identity_map_has_two_fixed_points, 否)；依完整明示資料獨立重算；Picard orbit、unique fixed point與geometric tail bound使用exact arithmetic；q=1、非self-map、noncomplete或sampled-pairs不足；finite model不取代一般定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r01-contraction-mapping-theorem-0084/)

壓縮映射定理 · qf-mod47-contract-boundary · candidate





## 85. 壓縮映射定理

完整metric、total self-map與forall-pairs q<1 contraction責任。操作=contract-boundary；資料={"mode":"non_self_map","scale":10}。請依 [mode, scale, mapping_description, theorem_application_claim] 欄序回答。

q=1、非self-map、非complete與sampled-pairs的6/4/6/6欄角色不同。sampled_pairs只保留來源的範圍敘述，沒有供應可重算的完整反例metric/map。

查看答案與解釋(non_self_map, 10, T_maps_one_point_outside_X, 否)

Wave6第十層核對=(non_self_map, 10, T_maps_one_point_outside_X, 否)；依完整明示資料獨立重算；Picard orbit、unique fixed point與geometric tail bound使用exact arithmetic；q=1、非self-map、noncomplete或sampled-pairs不足；finite model不取代一般定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r01-contraction-mapping-theorem-0085/)

壓縮映射定理 · qf-mod47-contract-boundary · candidate





## 86. 壓縮映射定理

完整metric、total self-map與forall-pairs q<1 contraction責任。操作=contract-boundary；資料={"mode":"noncomplete_space","scale":11}。請依 [mode, space_description, mapping_description, outside_fixed_point, q_as_fraction, theorem_application_claim] 欄序回答。

q=1、非self-map、非complete與sampled-pairs的6/4/6/6欄角色不同。sampled_pairs只保留來源的範圍敘述，沒有供應可重算的完整反例metric/map。

查看答案與解釋(noncomplete_space, X=(0,11), T(x)=(x+11)/2, fixed_point=11_outside_X, [1, 2], 否)

Wave6第十層核對=(noncomplete_space, X=(0,11), T(x)=(x+11)/2, fixed_point=11_outside_X, [1, 2], 否)；依完整明示資料獨立重算；Picard orbit、unique fixed point與geometric tail bound使用exact arithmetic；q=1、非self-map、noncomplete或sampled-pairs不足；finite model不取代一般定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r01-contraction-mapping-theorem-0086/)

壓縮映射定理 · qf-mod47-contract-boundary · candidate





## 87. 壓縮映射定理

完整metric、total self-map與forall-pairs q<1 contraction責任。操作=contract-boundary；資料={"mode":"sampled_pairs","scale":12}。請依 [mode, scale, sampled_pair_result, unchecked_pair_statement, global_contraction_claim, boundary] 欄序回答。

q=1、非self-map、非complete與sampled-pairs的6/4/6/6欄角色不同。sampled_pairs只保留來源的範圍敘述，沒有供應可重算的完整反例metric/map。

查看答案與解釋(sampled_pairs, 12, checked_pairs_pass, one_unchecked_pair_violates_global_bound, 否, sampled_pairs_do_not_prove_global_contraction)

Wave6第十層核對=(sampled_pairs, 12, checked_pairs_pass, one_unchecked_pair_violates_global_bound, 否, sampled_pairs_do_not_prove_global_contraction)；依完整明示資料獨立重算；Picard orbit、unique fixed point與geometric tail bound使用exact arithmetic；q=1、非self-map、noncomplete或sampled-pairs不足；finite model不取代一般定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r01-contraction-mapping-theorem-0087/)

壓縮映射定理 · qf-mod47-contract-boundary · candidate





## 88. 壓縮映射定理

完整metric、total self-map與forall-pairs q<1 contraction責任。操作=contract-boundary；資料={"mode":"q_equal_one","scale":13}。請依 [mode, scale, metric_description, q, fixed_point_counterexample, theorem_application_claim] 欄序回答。

q=1、非self-map、非complete與sampled-pairs的6/4/6/6欄角色不同。sampled_pairs只保留來源的範圍敘述，沒有供應可重算的完整反例metric/map。

查看答案與解釋(q_equal_one, 13, two_point_metric, 1, identity_map_has_two_fixed_points, 否)

Wave6第十層核對=(q_equal_one, 13, two_point_metric, 1, identity_map_has_two_fixed_points, 否)；依完整明示資料獨立重算；Picard orbit、unique fixed point與geometric tail bound使用exact arithmetic；q=1、非self-map、noncomplete或sampled-pairs不足；finite model不取代一般定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r01-contraction-mapping-theorem-0088/)

壓縮映射定理 · qf-mod47-contract-boundary · candidate





## 89. 壓縮映射定理

完整metric、total self-map與forall-pairs q<1 contraction責任。操作=contract-boundary；資料={"mode":"non_self_map","scale":14}。請依 [mode, scale, mapping_description, theorem_application_claim] 欄序回答。

q=1、非self-map、非complete與sampled-pairs的6/4/6/6欄角色不同。sampled_pairs只保留來源的範圍敘述，沒有供應可重算的完整反例metric/map。

查看答案與解釋(non_self_map, 14, T_maps_one_point_outside_X, 否)

Wave6第十層核對=(non_self_map, 14, T_maps_one_point_outside_X, 否)；依完整明示資料獨立重算；Picard orbit、unique fixed point與geometric tail bound使用exact arithmetic；q=1、非self-map、noncomplete或sampled-pairs不足；finite model不取代一般定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r01-contraction-mapping-theorem-0089/)

壓縮映射定理 · qf-mod47-contract-boundary · candidate





## 90. 壓縮映射定理

完整metric、total self-map與forall-pairs q<1 contraction責任。操作=contract-boundary；資料={"mode":"noncomplete_space","scale":15}。請依 [mode, space_description, mapping_description, outside_fixed_point, q_as_fraction, theorem_application_claim] 欄序回答。

q=1、非self-map、非complete與sampled-pairs的6/4/6/6欄角色不同。sampled_pairs只保留來源的範圍敘述，沒有供應可重算的完整反例metric/map。

查看答案與解釋(noncomplete_space, X=(0,15), T(x)=(x+15)/2, fixed_point=15_outside_X, [1, 2], 否)

Wave6第十層核對=(noncomplete_space, X=(0,15), T(x)=(x+15)/2, fixed_point=15_outside_X, [1, 2], 否)；依完整明示資料獨立重算；Picard orbit、unique fixed point與geometric tail bound使用exact arithmetic；q=1、非self-map、noncomplete或sampled-pairs不足；finite model不取代一般定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r01-contraction-mapping-theorem-0090/)

壓縮映射定理 · qf-mod47-contract-boundary · candidate





## 91. 壓縮映射定理

完整metric、total self-map與forall-pairs q<1 contraction責任。操作=contract-boundary；資料={"mode":"sampled_pairs","scale":16}。請依 [mode, scale, sampled_pair_result, unchecked_pair_statement, global_contraction_claim, boundary] 欄序回答。

q=1、非self-map、非complete與sampled-pairs的6/4/6/6欄角色不同。sampled_pairs只保留來源的範圍敘述，沒有供應可重算的完整反例metric/map。

查看答案與解釋(sampled_pairs, 16, checked_pairs_pass, one_unchecked_pair_violates_global_bound, 否, sampled_pairs_do_not_prove_global_contraction)

Wave6第十層核對=(sampled_pairs, 16, checked_pairs_pass, one_unchecked_pair_violates_global_bound, 否, sampled_pairs_do_not_prove_global_contraction)；依完整明示資料獨立重算；Picard orbit、unique fixed point與geometric tail bound使用exact arithmetic；q=1、非self-map、noncomplete或sampled-pairs不足；finite model不取代一般定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r01-contraction-mapping-theorem-0091/)

壓縮映射定理 · qf-mod47-contract-boundary · candidate





## 92. 壓縮映射定理

完整metric、total self-map與forall-pairs q<1 contraction責任。操作=contract-boundary；資料={"mode":"q_equal_one","scale":17}。請依 [mode, scale, metric_description, q, fixed_point_counterexample, theorem_application_claim] 欄序回答。

q=1、非self-map、非complete與sampled-pairs的6/4/6/6欄角色不同。sampled_pairs只保留來源的範圍敘述，沒有供應可重算的完整反例metric/map。

查看答案與解釋(q_equal_one, 17, two_point_metric, 1, identity_map_has_two_fixed_points, 否)

Wave6第十層核對=(q_equal_one, 17, two_point_metric, 1, identity_map_has_two_fixed_points, 否)；依完整明示資料獨立重算；Picard orbit、unique fixed point與geometric tail bound使用exact arithmetic；q=1、非self-map、noncomplete或sampled-pairs不足；finite model不取代一般定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r01-contraction-mapping-theorem-0092/)

壓縮映射定理 · qf-mod47-contract-boundary · candidate





## 93. 壓縮映射定理

完整metric、total self-map與forall-pairs q<1 contraction責任。操作=contract-boundary；資料={"mode":"non_self_map","scale":18}。請依 [mode, scale, mapping_description, theorem_application_claim] 欄序回答。

q=1、非self-map、非complete與sampled-pairs的6/4/6/6欄角色不同。sampled_pairs只保留來源的範圍敘述，沒有供應可重算的完整反例metric/map。

查看答案與解釋(non_self_map, 18, T_maps_one_point_outside_X, 否)

Wave6第十層核對=(non_self_map, 18, T_maps_one_point_outside_X, 否)；依完整明示資料獨立重算；Picard orbit、unique fixed point與geometric tail bound使用exact arithmetic；q=1、非self-map、noncomplete或sampled-pairs不足；finite model不取代一般定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r01-contraction-mapping-theorem-0093/)

壓縮映射定理 · qf-mod47-contract-boundary · candidate





## 94. 壓縮映射定理

完整metric、total self-map與forall-pairs q<1 contraction責任。操作=contract-boundary；資料={"mode":"noncomplete_space","scale":19}。請依 [mode, space_description, mapping_description, outside_fixed_point, q_as_fraction, theorem_application_claim] 欄序回答。

q=1、非self-map、非complete與sampled-pairs的6/4/6/6欄角色不同。sampled_pairs只保留來源的範圍敘述，沒有供應可重算的完整反例metric/map。

查看答案與解釋(noncomplete_space, X=(0,19), T(x)=(x+19)/2, fixed_point=19_outside_X, [1, 2], 否)

Wave6第十層核對=(noncomplete_space, X=(0,19), T(x)=(x+19)/2, fixed_point=19_outside_X, [1, 2], 否)；依完整明示資料獨立重算；Picard orbit、unique fixed point與geometric tail bound使用exact arithmetic；q=1、非self-map、noncomplete或sampled-pairs不足；finite model不取代一般定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r01-contraction-mapping-theorem-0094/)

壓縮映射定理 · qf-mod47-contract-boundary · candidate





## 95. 壓縮映射定理

完整metric、total self-map與forall-pairs q<1 contraction責任。操作=contract-boundary；資料={"mode":"sampled_pairs","scale":20}。請依 [mode, scale, sampled_pair_result, unchecked_pair_statement, global_contraction_claim, boundary] 欄序回答。

q=1、非self-map、非complete與sampled-pairs的6/4/6/6欄角色不同。sampled_pairs只保留來源的範圍敘述，沒有供應可重算的完整反例metric/map。

查看答案與解釋(sampled_pairs, 20, checked_pairs_pass, one_unchecked_pair_violates_global_bound, 否, sampled_pairs_do_not_prove_global_contraction)

Wave6第十層核對=(sampled_pairs, 20, checked_pairs_pass, one_unchecked_pair_violates_global_bound, 否, sampled_pairs_do_not_prove_global_contraction)；依完整明示資料獨立重算；Picard orbit、unique fixed point與geometric tail bound使用exact arithmetic；q=1、非self-map、noncomplete或sampled-pairs不足；finite model不取代一般定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r01-contraction-mapping-theorem-0095/)

壓縮映射定理 · qf-mod47-contract-boundary · candidate





## 96. 壓縮映射定理

完整metric、total self-map與forall-pairs q<1 contraction責任。操作=contract-boundary；資料={"mode":"q_equal_one","scale":21}。請依 [mode, scale, metric_description, q, fixed_point_counterexample, theorem_application_claim] 欄序回答。

q=1、非self-map、非complete與sampled-pairs的6/4/6/6欄角色不同。sampled_pairs只保留來源的範圍敘述，沒有供應可重算的完整反例metric/map。

查看答案與解釋(q_equal_one, 21, two_point_metric, 1, identity_map_has_two_fixed_points, 否)

Wave6第十層核對=(q_equal_one, 21, two_point_metric, 1, identity_map_has_two_fixed_points, 否)；依完整明示資料獨立重算；Picard orbit、unique fixed point與geometric tail bound使用exact arithmetic；q=1、非self-map、noncomplete或sampled-pairs不足；finite model不取代一般定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r01-contraction-mapping-theorem-0096/)

壓縮映射定理 · qf-mod47-contract-boundary · candidate





## 97. 壓縮映射定理

完整metric、total self-map與forall-pairs q<1 contraction責任。操作=contract-boundary；資料={"mode":"non_self_map","scale":22}。請依 [mode, scale, mapping_description, theorem_application_claim] 欄序回答。

q=1、非self-map、非complete與sampled-pairs的6/4/6/6欄角色不同。sampled_pairs只保留來源的範圍敘述，沒有供應可重算的完整反例metric/map。

查看答案與解釋(non_self_map, 22, T_maps_one_point_outside_X, 否)

Wave6第十層核對=(non_self_map, 22, T_maps_one_point_outside_X, 否)；依完整明示資料獨立重算；Picard orbit、unique fixed point與geometric tail bound使用exact arithmetic；q=1、非self-map、noncomplete或sampled-pairs不足；finite model不取代一般定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r01-contraction-mapping-theorem-0097/)

壓縮映射定理 · qf-mod47-contract-boundary · candidate





## 98. 壓縮映射定理

完整metric、total self-map與forall-pairs q<1 contraction責任。操作=contract-boundary；資料={"mode":"noncomplete_space","scale":23}。請依 [mode, space_description, mapping_description, outside_fixed_point, q_as_fraction, theorem_application_claim] 欄序回答。

q=1、非self-map、非complete與sampled-pairs的6/4/6/6欄角色不同。sampled_pairs只保留來源的範圍敘述，沒有供應可重算的完整反例metric/map。

查看答案與解釋(noncomplete_space, X=(0,23), T(x)=(x+23)/2, fixed_point=23_outside_X, [1, 2], 否)

Wave6第十層核對=(noncomplete_space, X=(0,23), T(x)=(x+23)/2, fixed_point=23_outside_X, [1, 2], 否)；依完整明示資料獨立重算；Picard orbit、unique fixed point與geometric tail bound使用exact arithmetic；q=1、非self-map、noncomplete或sampled-pairs不足；finite model不取代一般定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r01-contraction-mapping-theorem-0098/)

壓縮映射定理 · qf-mod47-contract-boundary · candidate





## 99. 壓縮映射定理

完整metric、total self-map與forall-pairs q<1 contraction責任。操作=contract-boundary；資料={"mode":"sampled_pairs","scale":24}。請依 [mode, scale, sampled_pair_result, unchecked_pair_statement, global_contraction_claim, boundary] 欄序回答。

q=1、非self-map、非complete與sampled-pairs的6/4/6/6欄角色不同。sampled_pairs只保留來源的範圍敘述，沒有供應可重算的完整反例metric/map。

查看答案與解釋(sampled_pairs, 24, checked_pairs_pass, one_unchecked_pair_violates_global_bound, 否, sampled_pairs_do_not_prove_global_contraction)

Wave6第十層核對=(sampled_pairs, 24, checked_pairs_pass, one_unchecked_pair_violates_global_bound, 否, sampled_pairs_do_not_prove_global_contraction)；依完整明示資料獨立重算；Picard orbit、unique fixed point與geometric tail bound使用exact arithmetic；q=1、非self-map、noncomplete或sampled-pairs不足；finite model不取代一般定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r01-contraction-mapping-theorem-0099/)

壓縮映射定理 · qf-mod47-contract-boundary · candidate





## 100. 壓縮映射定理

完整metric、total self-map與forall-pairs q<1 contraction責任。操作=contract-boundary；資料={"mode":"q_equal_one","scale":25}。請依 [mode, scale, metric_description, q, fixed_point_counterexample, theorem_application_claim] 欄序回答。

q=1、非self-map、非complete與sampled-pairs的6/4/6/6欄角色不同。sampled_pairs只保留來源的範圍敘述，沒有供應可重算的完整反例metric/map。

查看答案與解釋(q_equal_one, 25, two_point_metric, 1, identity_map_has_two_fixed_points, 否)

Wave6第十層核對=(q_equal_one, 25, two_point_metric, 1, identity_map_has_two_fixed_points, 否)；依完整明示資料獨立重算；Picard orbit、unique fixed point與geometric tail bound使用exact arithmetic；q=1、非self-map、noncomplete或sampled-pairs不足；finite model不取代一般定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r01-contraction-mapping-theorem-0100/)

壓縮映射定理 · qf-mod47-contract-boundary · candidate



[原始題目 JSONL](https://ocme.evemisslab.com/data/questions/batches/batch-20261015-advance-20261116-r01-contraction-mapping-theorem-foundations/questions.jsonl) · [驗收報告](https://ocme.evemisslab.com/data/questions/batches/batch-20261015-advance-20261116-r01-contraction-mapping-theorem-foundations/validation-report.json)